Install Supabase CLI from npm (#442)

## Summary
- install the Supabase CLI through the `supabase` npm package instead of
GitHub release archives
- support npm-backed `latest`, `beta`, and fixed published versions,
with root lockfile detection preserved
- remove the `github-token` input and use Node.js/npm without clobbering
an already configured Node.js 20+ runtime
- update CI/docs for the v3 action contract and remove stale license
cache entries for removed dependencies

Addresses CLI-1480:
https://linear.app/supabase/issue/CLI-1480/source-cli-install-from-npm-registry

No earlier pull request found to supersede.

## Validation
- `bun run ci`
- real npm install spot checks for `supabase@latest`, `supabase@beta`,
`supabase@1.178.2`, `supabase@2.33.0`, and legacy `supabase@1.15.1`
preinstall handling
- external fixture run:
https://github.com/jgoux/setup-cli-testing/actions/runs/28656824691
- hosted runners: Ubuntu, macOS, and Windows for `latest`, `beta`,
`1.178.2`, and `2.33.0`
  - package-lock detection: resolved and installed `supabase@2.108.0`
  - legacy preinstall: installed `supabase@1.15.1`
- Node preservation: kept a caller-provided Node.js 22 runtime active
after the action
- Alpine 3.20 container: `latest`, `beta`, and `2.100.0`, including
Node.js 20+ and runtime dependency checks
  - Alpine 3.18 container: rejected Node.js 18 with a clear setup error

docs/index.md

@@ -7,7 +7,12 @@ The action supports `ubuntu-latest`, `windows-latest`, and `macos-latest`, and
 adds the requested `supabase` version to `PATH` for the rest of the job.
 
 If `version` is omitted, the action checks the repository root for `bun.lock`,
-`pnpm-lock.yaml`, or `package-lock.json` and otherwise falls back to `latest`.
+`pnpm-lock.yaml`, or `package-lock.json` and otherwise falls back to npm
+`latest`.
+
+The action uses an existing Node.js/npm runtime when one is already available,
+and requires Node.js 20 or newer. On non-musl runners without Node.js or npm, it
+provisions them internally. Runners only need network access to the npm registry.
 
 ## Quick Start
 
@@ -24,19 +29,27 @@ jobs:
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v6
-      - uses: supabase/setup-cli@v2
+      - uses: supabase/setup-cli@v3
       - run: supabase init
       - run: supabase db start
 ```
 
-To pin a specific CLI version:
+To pin a fixed npm-published CLI version:
 
 ```yaml
-- uses: supabase/setup-cli@v2
+- uses: supabase/setup-cli@v3
   with:
     version: 2.84.2
 ```
 
+To test the current beta release:
+
+```yaml
+- uses: supabase/setup-cli@v3
+  with:
+    version: beta
+```
+
 ## Resources
 
 - **Source Code**: <https://github.com/supabase/setup-cli>