docs: implications of mutating cookies in server actions (#83691)

Ref: #83481 Closes:
https://linear.app/vercel/issue/DOC-5070/mutating-cookies-invalidates-router-cache

Making sure those using cookies in server actions, know that the server
tree is re-rendered and merged with the current client tree.

Author: icyJoseph

docs/01-app/01-getting-started/08-updating-data.mdx

@@ -393,7 +393,11 @@ Calling `redirect` [throws](/docs/app/api-reference/functions/redirect#behavior)
 
 ### Cookies
 
-You can `get`, `set`, and `delete` cookies inside a Server Action using the [`cookies`](/docs/app/api-reference/functions/cookies) API:
+You can `get`, `set`, and `delete` cookies inside a Server Action using the [`cookies`](/docs/app/api-reference/functions/cookies) API.
+
+When you [set or delete](/docs/app/api-reference/functions/cookies#understanding-cookie-behavior-in-server-actions) a cookie in a Server Action, Next.js re-renders the current page and its layouts on the server so the **UI reflects the new cookie value**.
+
+> **Good to know**: The server update applies to the current React tree, re-rendering, mounting, or unmounting components, as needed. Client state is preserved for re-rendered components, and effects re-run if their dependencies changed.
 
 ```ts filename="app/actions.ts" switcher
 'use server'

docs/01-app/03-api-reference/04-functions/cookies.mdx

@@ -82,6 +82,14 @@ When working with cookies in Server Components, it's important to understand tha
 
 The server can only send instructions (via `Set-Cookie` headers) to tell the browser to store cookies - the actual storage happens on the client side. This is why cookie operations that modify state (`.set`, `.delete`, `.clear`) must be performed in a Route Handler or Server Action where the response headers can be properly set.
 
+## Understanding Cookie Behavior in Server Actions
+
+After you set or delete a cookie in a Server Action, Next.js re-renders the current page and its layouts on the server so the UI reflects the new cookie value. See the [Caching guide](/docs/app/guides/caching#cookies).
+
+The UI is not unmounted, but effects that depend on data coming from the server will re-run.
+
+To refresh cached data too, call [`revalidatePath`](/docs/app/api-reference/functions/revalidatePath) or [`revalidateTag`](/docs/app/api-reference/functions/revalidateTag) inside the action.
+
 ## Examples
 
 ### Getting a cookie