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

bun.lock

@@ -6,7 +6,6 @@
       "name": "setup-cli",
       "dependencies": {
         "@actions/core": "^3.0.1",
-        "@actions/tool-cache": "^4.0.0",
       },
       "devDependencies": {
         "@tsconfig/bun": "^1.0.10",
@@ -27,8 +26,6 @@
 
     "@actions/io": ["@actions/io@3.0.2", "", {}, "sha512-nRBchcMM+QK1pdjO7/idu86rbJI5YHUKCvKs0KxnSYbVe3F51UfGxuZX4Qy/fWlp6l7gWFwIkrOzN+oUK03kfw=="],
 
-    "@actions/tool-cache": ["@actions/tool-cache@4.0.0", "", { "dependencies": { "@actions/core": "^3.0.0", "@actions/exec": "^3.0.0", "@actions/http-client": "^4.0.0", "@actions/io": "^3.0.0", "semver": "^7.7.3" } }, "sha512-L8P9HbXvpvqjZDveb/fdsa55IVC0trfPgQ4ZwGo6r5af6YDVdM9vMGPZ7rgY2fAT9gGj4PSYd6bYlg3p3jD78A=="],
-
     "@oxfmt/binding-android-arm-eabi": ["@oxfmt/binding-android-arm-eabi@0.49.0", "", { "os": "android", "cpu": "arm" }, "sha512-HbifJ84prIh9+55CTPAU35JdRQrwg47y16cGerCC+iejSKOuHXYo2WDql6l7cQlzrYVtc3f4UWY+dBj2lRmOeA=="],
 
     "@oxfmt/binding-android-arm64": ["@oxfmt/binding-android-arm64@0.49.0", "", { "os": "android", "cpu": "arm64" }, "sha512-Ef7SKJqAaH2d7E6eXZZa2OffIShbhFMxnGK0zd93p4qiyTJr75B0qf7lrPD+qQOwcf04BrjYJ0JUxq8d5+yZwg=="],
@@ -147,8 +144,6 @@
 
     "oxlint-tsgolint": ["oxlint-tsgolint@0.22.1", "", { "optionalDependencies": { "@oxlint-tsgolint/darwin-arm64": "0.22.1", "@oxlint-tsgolint/darwin-x64": "0.22.1", "@oxlint-tsgolint/linux-arm64": "0.22.1", "@oxlint-tsgolint/linux-x64": "0.22.1", "@oxlint-tsgolint/win32-arm64": "0.22.1", "@oxlint-tsgolint/win32-x64": "0.22.1" }, "bin": { "tsgolint": "bin/tsgolint.js" } }, "sha512-YUSGSLUnoolsu8gxISEDio3q1rtsCozwfOzASUn3DT2mR2EeQ93uEEnen7s+6LpF+lyTQFln1pQfqwBh/fsVEg=="],
 
-    "semver": ["semver@7.7.4", "", { "bin": { "semver": "bin/semver.js" } }, "sha512-vFKC2IEtQnVhpT78h1Yp8wzwrf8CM+MzKMHGJZfBtzhZNycRFnXsHk6E5TxIkkMsgNS7mdX3AGB7x2QM2di4lA=="],
-
     "tinypool": ["tinypool@2.1.0", "", {}, "sha512-Pugqs6M0m7Lv1I7FtxN4aoyToKg1C4tu+/381vH35y8oENM/Ai7f7C4StcoK4/+BSw9ebcS8jRiVrORFKCALLw=="],
 
     "tunnel": ["tunnel@0.0.6", "", {}, "sha512-1h/Lnq9yajKY2PEbBadPXj3VxsDDu844OnaAo52UVmIzIvwwtBPIuNvkjuzBlTWpfJyUbG3ez0KSBibQkj4ojg=="],
@@ -156,7 +151,5 @@
     "undici": ["undici@6.24.1", "", {}, "sha512-sC+b0tB1whOCzbtlx20fx3WgCXwkW627p4EA9uM+/tNNPkSS+eSEld6pAs9nDv7WbY1UUljBMYPtu9BCOrCWKA=="],
 
     "undici-types": ["undici-types@6.21.0", "", {}, "sha512-iwDZqg0QAGrg9Rav5H4n0M64c3mkR59cJ6wQp+7C4nI0gsmExaedaYLNO44eT4AtBBwjbTiGPMlt2Md0T9H9JQ=="],
-
-    "@actions/tool-cache/@actions/core": ["@actions/core@3.0.0", "", { "dependencies": { "@actions/exec": "^3.0.0", "@actions/http-client": "^4.0.0" } }, "sha512-zYt6cz+ivnTmiT/ksRVriMBOiuoUpDCJJlZ5KPl2/FRdvwU3f7MPh9qftvbkXJThragzUZieit2nyHUyw53Seg=="],
   }
 }