test: add self-contained integration environment

Separate schema migrations from environment-specific fixtures, run the full API workflow against a disposable PostgreSQL Testcontainer, and provide seeded development and UI test environments.

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/migrations/00004_question_reference_answer.sql

@@ -2,12 +2,5 @@
 ALTER TABLE questions
     ADD COLUMN reference_answer TEXT NOT NULL DEFAULT '';
 
-UPDATE questions
-SET reference_answer = CASE
-    WHEN type = 'open' THEN 'Use context cancellation, stop accepting work, drain active requests, and close dependencies within a deadline.'
-    WHEN type = 'code_review' THEN 'Identify unstable dependencies or state updates that cause avoidable renders and propose memoization only where measured.'
-    ELSE reference_answer
-END;
-
 -- +goose Down
 ALTER TABLE questions DROP COLUMN reference_answer;