uv: continue Python installation after bootstrapping uv

[Eleanor Boyd (eleanorjboyd)]

Fixes #1871.

Problem

When uv's install directory is not already on the extension host's PATH, the official installer can succeed but the subsequent bare uv --version lookup still fails. Python installation then stops at uvNotOnPath.

Updating shell startup files does not update the already-running extension host's environment. Resetting the availability cache alone cannot fix this.

Changes

• Retain the installed uv executable for the current extension-host session, honoring the standalone installer's explicit, legacy, unmanaged, XDG, and default destinations.
• Use that executable consistently for availability checks, Python installation, installed/available Python version listing, and subsequent shared uv operations.
• Preserve the executable across availability-cache resets and prevent an older in-flight check from overwriting a newly reset cache.
• Leave process PATH and the integrated terminal's PATH unchanged.
• Add 23 regression cases covering the complete bootstrap handoff, failures, inline-script version lookup, cache behavior, and Windows/POSIX destination naming. Update the uv behavior documentation.

Validation

• npm run compile-tests
• npm run compile
• npm run unittest -- --grep 'uvPythonInstaller|Helpers|Pip and UV command parsing|InlineScriptEnvManager' — 518 passing
• ESLint on all four changed TypeScript files
• git diff --check

Real installation checks on macOS arm64

Used isolated VS Code development hosts, real consent dialogs/tasks, uv 0.12.21, and real Python 3.11.15 installations. All fixture home paths included spaces.

Case	Before	With this change
Fresh uv installation; destination absent from extension-host PATH	uv task succeeds, then uvNotOnPath; no Python installation	uv and Python tasks succeed; returned Python executes
Fresh installation; destination already on PATH	Succeeds	Succeeds
New host reusing installed uv with explicitly corrected PATH	Succeeds	Succeeds

In the fixed missing-PATH case, bare uv --version still returns ENOENT, while the extension successfully installs and locates Python using the absolute executable path. This confirms the fix does not depend on PATH mutation.

Reviewer notes

• Native Windows integration was not run; Windows destination/naming behavior has unit coverage.
• The real-host harness directly invokes the compiled production installer modules and exercises real VS Code tasks/UI. It does not exercise automatic no-Python detection or the bundled extension's full activation path.
• Related open PR uv: install uv before listing Python versions #1834 changes the Global-create prerequisite flow in the same installer file. This PR preserves installUv's boolean return contract; the two changes address different steps of the workflow.