chore: upgrade Changesets to v3 (#1102)

Upgrades `@changesets/cli` from 2.31.0 to 3.0.0 and `changesets/action`
from v1 to v2 (v1 is pinned to the Changesets v2 packages).

Changesets v3 is ESM-only and requires Node `^22.11 || ^24 || >=26`, so
`.node-version` moves from `lts/iron` (20) to `lts/jod` (22) and the root
`engines.node` floor moves from `>=18` to `>=22.11`.

Two v3 defaults would otherwise change release output silently:

- Private packages are no longer versioned by default. This repo has been
  versioning `vercel-storage-integration-test-suite`, so
  `privatePackages: { version: true, tag: false }` is now set explicitly to
  keep the v2 behaviour.
- Releasing a package no longer forces a `major` bump on workspace packages
  that declare it as a peer dependency; they get a `patch` when the peer
  range has to be widened and nothing when it still matches. No package in
  this workspace declares another workspace package as a peer dependency
  today, so version math is unchanged — `.changeset/README.md` documents the
  new rule for when that changes.

`changesets/action@v2` renamed the inputs used here (`publish` ->
`publish-script`, `version` -> `version-script`) and no longer reads the
token from the `GITHUB_TOKEN` environment variable, so it is passed through
the `github-token` input. Pushing release commits and tags through the
GitHub API is the v2 default, which replaces `commitMode: github-api`.

Co-authored-by: vercel[bot] <35613825+vercel[bot]@users.noreply.github.com>
Co-authored-by: Dominik Ferber <1765075+dferber90@users.noreply.github.com>