chore(0.76): set up proper publishing pipeline

[Saadnajmi]

Summary:

Backport #2266 to 0.76-stable.

We have a new release pipeline, but on our main branch we don't publish nightlies yet so it's not used. We also have issues with our 0.76-stable publishes, so let's just backport the release pipeline so we can better test it against a stable branch.

Some observations / learnings:

• To update nx.json with node .ado/scripts/prepublish-check.mjs --update (as documented, the script expects the current branch to be 0.xx-stable. Usually we are in a staging branch (e.x: sanajmi/merge-to-xx-stable-cutoff) so it didn't work. I had to make a temporary branch named 0.xx-stable locally to update our config.
• With yarn nx release --dry-run (very useful btw!) I noticed we aren't setting the version number in native files (RCTVersion.h, etc), only package.json files. To account for this, I locally ran node scripts/releases/set-rn-artifacts-version.js -b release -v 0.76.5 (knowing the next published version will be 0.76.5 and committed the result.
• From the dry run, I noticed we will also update our local copies of @react-native/oss-library-example and @react-native/tester like so. These are local packages so it's fine, but it does remove the workspace:* that I added. That seems like a bug.

UPDATE packages/react-native-test-library/package.json [dry-run]

    "name": "@react-native/oss-library-example",
-   "version": "0.76.4",
+   "version": "0.76.5",
    "private": true,

      "@react-native/babel-preset": "0.76.3",
-     "react-native-macos": "workspace:*"
+     "react-native-macos": "0.76.5"
    },

UPDATE packages/rn-tester/package.json [dry-run]

    "name": "@react-native/tester",
-   "version": "0.76.4",
+   "version": "0.76.5",
    "private": true,

    "dependencies": {
-     "@react-native/oss-library-example": "workspace:*",
+     "@react-native/oss-library-example": "0.76.5",
      "@react-native/popup-menu-android": "workspace:*",

Test Plan:

Can't really test publish changes easily, we'll have to make followups.