Write requested python variant to pin file in uv init (#12870)

## Summary

Closes #12855

This PR also fixed an issue, where `python_request` was matched against
`PythonVersion::Default`. Previously, if `python_request` was `3.13t`,
it would match the last branch, triggering a download of the Python
version if it wasn't already installed.


https://github.com/astral-sh/uv/blob/6b7f60c1eaa840c2e933a0fb056ab46f99c991a5/crates/uv/src/commands/project/init.rs#L421-L448

```console
❯ uv init -v --managed-python --python 3.13t foo
DEBUG uv 0.6.14 (a4cec56 2025-04-09)
DEBUG Searching for Python 3.13t in managed installations
DEBUG Searching for managed installations at `/Users/Jo/.local/share/uv/python`
DEBUG Found managed installation `cpython-3.13.1-macos-aarch64-none`
DEBUG Found `cpython-3.13.1-macos-aarch64-none` at `/Users/Jo/.local/share/uv/python/cpython-3.13.1-macos-aarch64-none/bin/python3.13` (managed installations)
DEBUG Skipping interpreter at `/Users/Jo/.local/share/uv/python/cpython-3.13.1-macos-aarch64-none/bin/python3.13` from managed installations: does not satisfy request `3.13t`
DEBUG Skipping incompatible managed installation `cpython-3.12.8-macos-aarch64-none`
DEBUG Skipping incompatible managed installation `pypy-3.11.11-macos-aarch64-none`
DEBUG Requested Python not found, checking for available download...
DEBUG Acquired lock for `/Users/Jo/.local/share/uv/python`
DEBUG Using request timeout of 30s
INFO Fetching requested Python...
Downloading cpython-3.13.3+freethreaded-macos-aarch64-none (49.9MiB)
DEBUG Downloading https://github.com/astral-sh/python-build-standalone/releases/download/20250409/cpython-3.13.3%2B20250409-aarch64-apple-darwin-freethreaded%2Bpgo%2Blto-full.tar.zst to temporary location: /Users/Jo/.local/share/uv/python/.temp/.tmpfoOLkE
DEBUG Extracting cpython-3.13.3%2B20250409-aarch64-apple-darwin-freethreaded%2Bpgo%2Blto-full.tar.zst
 Downloaded cpython-3.13.3+freethreaded-macos-aarch64-none
DEBUG Moving /Users/Jo/.local/share/uv/python/.temp/.tmpfoOLkE/python/install to /Users/Jo/.local/share/uv/python/cpython-3.13.3+freethreaded-macos-aarch64-none
DEBUG Released lock at `/Users/Jo/.local/share/uv/python/.lock`
DEBUG Writing Python versions to `/private/tmp/foo/.python-version`
Initialized project `foo` at `/private/tmp/foo`

❯ cat foo/.python-version
3.13
```

After this PR, uv will not try to download it:

```console
❯ uv python uninstall 3.13t
❯ cargo run -- init -v --managed-python --python 3.13t bar
DEBUG uv 0.6.14+15 (6b7f60c 2025-04-12)
DEBUG Writing Python versions to `/private/tmp/bar/.python-version`
Initialized project `bar` at `/private/tmp/bar`

❯ cat bar/.python_version
3.13t
```

Author: j178

crates/uv/src/commands/project/init.rs

@@ -370,21 +370,15 @@ async fn init_project(
         // This can be arbitrary, i.e., not a version — in which case we may need to resolve the
         // interpreter
         match python_request {
-            PythonRequest::Version(VersionRequest::MajorMinor(
-                major,
-                minor,
-                PythonVariant::Default,
-            )) => {
+            PythonRequest::Version(VersionRequest::MajorMinor(major, minor, variant)) => {
                 let requires_python = RequiresPython::greater_than_equal_version(&Version::new([
                     u64::from(major),
                     u64::from(minor),
                 ]));
 
                 let python_request = if pin_python {
                     Some(PythonRequest::Version(VersionRequest::MajorMinor(
-                        major,
-                        minor,
-                        PythonVariant::Default,
+                        major, minor, variant,
                     )))
                 } else {
                     None
@@ -396,7 +390,7 @@ async fn init_project(
                 major,
                 minor,
                 patch,
-                PythonVariant::Default,
+                variant,
             )) => {
                 let requires_python = RequiresPython::greater_than_equal_version(&Version::new([
                     u64::from(major),
@@ -406,19 +400,18 @@ async fn init_project(
 
                 let python_request = if pin_python {
                     Some(PythonRequest::Version(VersionRequest::MajorMinorPatch(
-                        major,
-                        minor,
-                        patch,
-                        PythonVariant::Default,
+                        major, minor, patch, variant,
                     )))
                 } else {
                     None
                 };
 
                 (requires_python, python_request)
             }
-            ref
-            python_request @ PythonRequest::Version(VersionRequest::Range(ref specifiers, _)) => {
+            ref python_request @ PythonRequest::Version(VersionRequest::Range(
+                ref specifiers,
+                variant,
+            )) => {
                 let requires_python = RequiresPython::from_specifiers(specifiers);
 
                 let python_request = if pin_python {
@@ -439,7 +432,7 @@ async fn init_project(
                     Some(PythonRequest::Version(VersionRequest::MajorMinor(
                         interpreter.python_major(),
                         interpreter.python_minor(),
-                        PythonVariant::Default,
+                        variant,
                     )))
                 } else {
                     None

crates/uv/tests/it/init.rs

@@ -3713,3 +3713,22 @@ fn init_without_description() -> Result<()> {
 
     Ok(())
 }
+
+/// Run `uv init --python 3.13t` to create a pin to a freethreaded Python.
+#[test]
+fn init_python_variant() -> Result<()> {
+    let context = TestContext::new("3.13");
+    uv_snapshot!(context.filters(), context.init().arg("foo").arg("--python").arg("3.13t"), @r###"
+    success: true
+    exit_code: 0
+    ----- stdout -----
+
+    ----- stderr -----
+    Initialized project `foo` at `[TEMP_DIR]/foo`
+    "###);
+
+    let python_version = fs_err::read_to_string(context.temp_dir.join("foo/.python-version"))?;
+    assert_eq!(python_version, "3.13t\n");
+
+    Ok(())
+}