docs: fix all 158 broken links (#5972)

Would obsolete #5965, #5918 if merged.

I listed the broken links on my end like this:

    # utilizing lychee
    # lychee doesn't support checking links recursively from a web page;
    # but we do have a kind of sitemap here that we can pass to it.
    cd tanstack-table/docs/
    lychee $(find . -name '*.md' | sed 's~./~https://tanstack.com/table/latest/docs/~;s/.md//')
    # for the local build; might also want `--timeout 60`
    lychee $(find . -name '*.md' | sed 's~./~http://localhost:3000/table/latest/docs/~;s/.md//')
    # sed's separator in 's/from/to/' can be changed to avoid escaping,
    # so 's~from~to~' has the same effect except slashes can stay as-is.
    # then s/.md// gets rid of the extension, completing the conversion
    # to deployed URLs.
    # (I'm explaining all this because I'm also scared by the xz takeover.)

There is some magic with relative links: "../" seems to navigate to
"../../" instead (???), while ./ is the current path. As a result every
replacement here is manually done and tested with lychee. Exceptional
cases are explained in the details section below.

When checking the result afterwards, there may be one broken link left
if locally only the /tanstack/tanstack.com and /tanstack/table
repositories are checked out:
from localhost:3000/table/latest/docs/guide/virtualization,
linking to localhost:3000/virtual/v3/docs/api/virtualizer.
This is an artifact of the way it's checked out.

Detailed changes:

docs/api/core/{cell,column,header-group,header,row,table}:
  link to /docs/guide/features currently link to /guide/features
  instead, and causes a redirect loop.
  This error is deployed right now: check eg.
  https://tanstack.com/table/latest/docs/api/core/cell
  and click the "table features" link.
  (This is not exceptional, just the first case I tackled.)

docs/guide/headers:
  Aside from fixing paths, also fix an incorrect reference to
  non-existant Column Resizing Guide at docs/guide/column-resizing;
  presumably this is misspelling for the Column Sizing Guide at
  docs/guide/column-sizing.

docs/guide/row-selection:
  Beyond fixing paths, also fix a missing /example/ in the vue example
  path.

Author: kisaragi-hiu

docs/api/core/cell.md

@@ -2,7 +2,7 @@
 title: Cell APIs
 ---
 
-These are **core** options and API properties for all cells. More options and API properties are available for other [table features](../../../guide/features).
+These are **core** options and API properties for all cells. More options and API properties are available for other [table features](../guide/features).
 
 ## Cell API
 

docs/api/core/column.md

@@ -2,7 +2,7 @@
 title: Column APIs
 ---
 
-These are **core** options and API properties for all columns. More options and API properties are available for other [table features](../../../guide/features).
+These are **core** options and API properties for all columns. More options and API properties are available for other [table features](../guide/features).
 
 ## Column API
 

docs/api/core/header-group.md

@@ -2,7 +2,7 @@
 title: HeaderGroup APIs
 ---
 
-These are **core** options and API properties for all header groups. More options and API properties may be available for other [table features](../../../guide/features).
+These are **core** options and API properties for all header groups. More options and API properties may be available for other [table features](../guide/features).
 
 ## Header Group API
 
@@ -30,4 +30,4 @@ The depth of the header group, zero-indexed based.
 type headers = Header<TData>[]
 ```
 
-An array of [Header](../header) objects that belong to this header group
+An array of [Header](../api/core/header) objects that belong to this header group

docs/api/core/header.md

@@ -2,7 +2,7 @@
 title: Header APIs
 ---
 
-These are **core** options and API properties for all headers. More options and API properties may be available for other [table features](../../../guide/features).
+These are **core** options and API properties for all headers. More options and API properties may be available for other [table features](../guide/features).
 
 ## Header API
 
@@ -38,15 +38,15 @@ The depth of the header, zero-indexed based.
 column: Column<TData>
 ```
 
-The header's associated [Column](../column) object
+The header's associated [Column](../api/core/column) object
 
 ### `headerGroup`
 
 ```tsx
 headerGroup: HeaderGroup<TData>
 ```
 
-The header's associated [HeaderGroup](../header-group) object
+The header's associated [HeaderGroup](../api/core/header-group) object
 
 ### `subHeaders`
 

docs/api/core/row.md

@@ -2,7 +2,7 @@
 title: Row APIs
 ---
 
-These are **core** options and API properties for all rows. More options and API properties are available for other [table features](../../../guide/features).
+These are **core** options and API properties for all rows. More options and API properties are available for other [table features](../guide/features).
 
 ## Row API
 
@@ -120,4 +120,4 @@ An array of the original subRows as returned by the `options.getSubRows` option.
 type getAllCells = () => Cell<TData>[]
 ```
 
-Returns all of the [Cells](../cell) for the row.
+Returns all of the [Cells](../api/core/cell) for the row.

docs/api/core/table.md

@@ -14,7 +14,7 @@ These functions are used to create a table. Which one you use depends on which f
 
 ## Options
 
-These are **core** options and API properties for the table. More options and API properties are available for other [table features](../../../guide/features).
+These are **core** options and API properties for the table. More options and API properties are available for other [table features](../guide/features).
 
 ### `data`
 
@@ -89,7 +89,7 @@ declare module '@tanstack/table-core' {
 }
 ```
 
-> 🧠 Think of this option as an arbitrary "context" for your table. This is a great way to pass arbitrary data or functions to your table without having to pass it to every thing the table touches. A good example is passing a locale object to your table to use for formatting dates, numbers, etc or even a function that can be used to update editable data like in the [editable-data example](../../../framework/react/examples/editable-data).
+> 🧠 Think of this option as an arbitrary "context" for your table. This is a great way to pass arbitrary data or functions to your table without having to pass it to every thing the table touches. A good example is passing a locale object to your table to use for formatting dates, numbers, etc or even a function that can be used to update editable data like in the [editable-data example](../framework/react/examples/editable-data).
 
 ### `state`
 

docs/api/features/filters.md

@@ -7,7 +7,7 @@ id: filters
 
 The Filtering API docs are now split into multiple API doc pages:
 
-- [Column Faceting](../column-faceting)
-- [Global Faceting](../global-faceting)
-- [Column Filtering](../column-filtering)
-- [Global Filtering](../global-filtering)
+- [Column Faceting](../api/features/column-faceting)
+- [Global Faceting](../api/features/global-faceting)
+- [Column Filtering](../api/features/column-filtering)
+- [Global Filtering](../api/features/global-filtering)

docs/api/features/global-filtering.md

@@ -25,7 +25,7 @@ export interface GlobalFilterTableState {
 
 ## Filter Functions
 
-You can use the same filter functions that are available for column filtering for global filtering. See the [Column Filtering APIs](../column-filtering) to learn more about filter functions.
+You can use the same filter functions that are available for column filtering for global filtering. See the [Column Filtering APIs](../api/features/column-filtering) to learn more about filter functions.
 
 #### Using Filter Functions
 

docs/api/features/pinning.md

@@ -7,5 +7,5 @@ id: pinning
 
 The pinning apis are now split into multiple api pages:
 
-- [Column Pinning](../column-pinning)
-- [Row Pinning](../row-pinning)
+- [Column Pinning](../api/features/column-pinning)
+- [Row Pinning](../api/features/row-pinning)

docs/api/features/row-selection.md

@@ -15,7 +15,7 @@ export type RowSelectionTableState = {
 }
 ```
 
-By default, the row selection state uses the index of each row as the row identifiers. Row selection state can instead be tracked with a custom unique row id by passing in a custom [getRowId](../../../api/core/table.md#getrowid) function to the the table.
+By default, the row selection state uses the index of each row as the row identifiers. Row selection state can instead be tracked with a custom unique row id by passing in a custom [getRowId](../core/table.md#getrowid) function to the the table.
 
 ## Table Options