Rework e2e tests (#36634)

- Replace the e2e tests initialization with a simple bash script,
removing the previous Go harness.
- `make test-e2e` is the single entry point. It always starts a fully
isolated ephemeral Gitea instance with its own temp directory, SQLite
database, and config — no interference with the developer's running
instance.
- A separate `gitea-e2e` binary is built via `EXECUTABLE_E2E` using
`TEST_TAGS` (auto-includes sqlite with `CGO_ENABLED=1`), keeping the
developer's regular `gitea` binary untouched.
- No more split into database-specific e2e tests. Test timeouts are
strict, can be relaxed later if needed.
- Simplified and streamlined the playwright config and test files.
- Remove all output generation of playwright and all references to
visual testing.
- Tests run on Chrome locally, Chrome + Firefox on CI.
- Simplified CI workflow — visible separate steps for frontend, backend,
and test execution.
- All exported env vars use `GITEA_TEST_E2E_*` prefix.
- Use `GITEA_TEST_E2E_FLAGS` to pass flags to playwright, e.g.
`GITEA_TEST_E2E_FLAGS="--ui" make test-e2e` for UI mode or
`GITEA_TEST_E2E_FLAGS="--headed" make test-e2e` for headed mode.
- Use `GITEA_TEST_E2E_DEBUG=1 make test-e2e` to show Gitea server
output.

---------

Signed-off-by: silverwind <me@silverwind.io>
Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

.gitignore

@@ -55,6 +55,7 @@ cpu.out
 *.log.*.gz
 
 /gitea
+/gitea-e2e
 /gitea-vet
 /debug
 /integrations.test
@@ -67,13 +68,9 @@ cpu.out
 /indexers
 /log
 /public/assets/img/avatar
+/tests/e2e-output
 /tests/integration/gitea-integration-*
 /tests/integration/indexers-*
-/tests/e2e/gitea-e2e-*
-/tests/e2e/indexers-*
-/tests/e2e/reports
-/tests/e2e/test-artifacts
-/tests/e2e/test-snapshots
 /tests/*.ini
 /tests/**/*.git/**/*.sample
 /node_modules