ci: shard tests and reduce redundant work (#37618)

Critical path ~25:42 → ~19:56 (−22%), ~0% CI minutes.

- `test-pgsql` shards 2-way. Branch protection: replace `test-pgsql`
with `test-pgsql-shards (1)` + `test-pgsql-shards (2)`; `test-unit`,
sqlite/mysql/mssql unchanged — pgsql dominates the critical path.
- `test-unit` runs `bindata` then `bindata gogit` sequentially.
cache-seeder pre-warms the race-instrumented test compile cache and the
integration test binary so PR jobs warm-start.
- Cache writes restricted to cache-seeder; PR jobs use
`actions/cache/restore`. Defends against PR cache poisoning and frees
the 10 GB cap from PR churn.
- `go-cache` action: dropped the `cache-name` input. One gobuild cache,
one golangci-lint cache. Seeder lint job restores but doesn't save
gobuild, so only one writer populates it.
- `tools/test-integration.sh` shards the integration binary via
`-test.list`; `TestMain` short-circuits DB init in list mode.

`TestAPILFSNotStarted` / `TestAPILFSLocksNotStarted` switched to
`test.MockVariableValue` — latent `setting.LFS.StartServer` global-state
leak uncovered by sharding.

---
This PR was written with the help of Claude Opus 4.7

---------

Signed-off-by: silverwind <me@silverwind.io>
Co-authored-by: Claude (Opus 4.7) <noreply@anthropic.com>
Co-authored-by: wxiaoguang <wxiaoguang@gmail.com>
Co-authored-by: Nicolas <bircni@icloud.com>

.github/workflows/pull-e2e-tests.yml

@@ -26,9 +26,6 @@ jobs:
           check-latest: true
           cache: false
       - uses: ./.github/actions/go-cache
-        with:
-          cache-name: e2e
-          build-cache: "false"
       - uses: pnpm/action-setup@0e279bb959325dab635dd2c09392533439d90093 # v6.0.8
       - uses: actions/setup-node@48b55a011bda9f5d6aeb4c2d9c7362e8dae4041e # v6.4.0
         with: