chore: remove committed binaries and scratch dirs; tighten .gitignore

- Remove committed Go binaries:
    backend/bin/api-server (~18 MB)
    backend/cmd (~18 MB)
    backend/api/rest/cmd/api-server (~18 MB)
- Remove scratch / build output dirs from the repo:
    out/, cache/, test-results/
- Extend .gitignore to cover these paths plus playwright-report/
  and coverage/ so they don't drift back in.

Total artifact weight removed: ~54 MB of binaries + small scratch files.

.gitignore

@@ -49,3 +49,16 @@ temp/
 *.test
 *.out
 go.work
+
+# Compiled Go binaries (built artifacts, not source)
+backend/bin/
+backend/api/rest/cmd/api-server
+backend/cmd
+
+# Tooling / scratch directories
+out/
+cache/
+test-results/
+playwright-report/
+.playwright/
+coverage/