Rework e2e test setup for full isolation

Always start an isolated ephemeral Gitea instance with its own temp
directory, SQLite database, and config file. This addresses review
feedback that using the developer's existing instance is unreliable.

- Rewrite test-e2e.sh to create a temp workdir, find a free port,
  write a minimal app.ini, start the server, and clean up on exit
- Build a separate gitea-e2e binary using TEST_TAGS (includes sqlite)
- Simplify CI workflow: remove manual app.ini, server start, and
  redundant build steps
- Rename all env vars to use GITEA_TEST_E2E_* prefix
- Rename test user from "e2e" to "e2e-user"

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Makefile

@@ -200,7 +200,7 @@ clean-all: clean ## delete backend, frontend and integration files
 
 .PHONY: clean
 clean: ## delete backend and integration files
-	rm -rf $(EXECUTABLE) $(DIST) $(BINDATA_DEST_WILDCARD) \
+	rm -rf $(EXECUTABLE) gitea-e2e $(DIST) $(BINDATA_DEST_WILDCARD) \
 		integrations*.test \
 		tests/integration/gitea-integration-* \
 		tests/integration/indexers-* \
@@ -534,8 +534,9 @@ playwright: deps-frontend
 	@$(NODE_VARS) pnpm exec playwright install $(if $(GITHUB_ACTIONS),,--with-deps) chromium $(PLAYWRIGHT_FLAGS)
 
 .PHONY: test-e2e
-test-e2e: playwright $(EXECUTABLE)
-	@EXECUTABLE=$(EXECUTABLE) ./tools/test-e2e.sh $(E2E_FLAGS)
+test-e2e: playwright
+	$(GO) build $(GOFLAGS) $(EXTRA_GOFLAGS) -tags '$(TEST_TAGS)' -ldflags '-s -w $(EXTLDFLAGS) $(LDFLAGS)' -o gitea-e2e
+	@EXECUTABLE=gitea-e2e ./tools/test-e2e.sh $(GITEA_TEST_E2E_FLAGS)
 
 .PHONY: bench-sqlite
 bench-sqlite: integrations.sqlite.test generate-ini-sqlite