fix(ai): persist Studio chat sessions across restarts

[PurplePrintAI]

Summary

• Persist AI conversations per project in the Studio userData profile, including turns, generated-image references, manual compaction state, and rewind checkpoints.
• Restore chats after a restart and open the newest conversation. Remove saved chats when their project is deleted.
• Save by temporary file plus atomic replacement. A corrupt history file remains untouched and surfaces an error instead of being silently replaced.

Why

Studio kept the chat session map only in the Electron main process. Closing the app erased every conversation even though the project file remained.

Verification

• Full unit suite: 191 files passed, 2,276 tests passed, 5 skipped.
• Final branch CI: https://github.com/PurplePrintAI/openscreen-subscription/actions/runs/36508357651 (success).
• Windows clean package: https://github.com/PurplePrintAI/openscreen-subscription/actions/runs/36508358033 (success; unsigned validation-only artifact).
• App and test TypeScript checks passed; lint passed with pre-existing warnings; production Vite bundle built.
• Added restart, image-message, checkpoint/rewind, compaction, deletion, corrupt-file, and latest-session UI tests.

Limitations and rollout

• Chats already lost on a previous restart cannot be recovered; earlier builds never wrote them to disk.
• Chat text and document checkpoints are local plaintext JSON in the Studio profile, separate from provider credentials.
• Windows candidate from the final commit was installed after a verified eight-project profile backup. One approved neutral Claude turn created two on-disk messages, and both reappeared in the QA project after a full app quit/relaunch. The project document hash remained unchanged. The installed app archive SHA-256 is ACBE40664CF189E3C5BCF60AD7B0B4DA38DC089C5E87F2E29645ED2F7602E5A7.
• The first manual CI run failed before Rust tests because Homebrew no longer bottled x265 for the macOS 14 runner; the follow-up commit switched that job to the supported macOS runner. The final CI run above passed.
• Stacked on feat: add ChatGPT subscription image scenes to Studio #7; merge feat: add ChatGPT subscription image scenes to Studio #7 first, then retarget this PR to fork/main before merging.