feat(web): integrate terminal details, thinking state and unarchive

[tt-a1i]

Web consumers cannot yet inspect exact Background Terminal evidence or Pi thinking levels, and archived Sessions cannot be restored through the API. This integrates the reviewed contributions from #389, #375 and the unarchive portion of #361 against current main.

• Add Session-scoped, exact-id terminal details with bounded UTF-8 output, explicit missing/unavailable responses and no private spill paths.
• Add read-only Pi thinking-level inspection with an explicit unknown fallback for unsupported controllers.
• Add idempotent unarchive using the existing atomic metadata transaction, preserving canonical Session JSONL and workspace grouping.

Main’s richer trust projection is preserved; #361’s inherited #360 trust changes are omitted. Host conflicts retain current trust and provider-authentication routes. These are backend capabilities; no browser panels or new model tools are added.

Related: #346, #348, #347. Supersedes the retained implementation portions of #389, #375 and #361.

Validation on f5bfec80c467a0763f3a1d4593b3adb292ea9331, based on main 4e767e433dd7f6c372b51f25cd5bce06179ab215:

• bun run check passed.
• bun run test: 1,457 Node tests passed, one skipped; 92 Vitest tests passed.
• Added integration coverage for authentication, thinking fallback, repeated/concurrent unarchive, adapter restart and unchanged canonical Session bytes.
• Two independent final source reviews found no P2 or higher issue.
• No installed Pi or manual browser acceptance is claimed.

Original contributors are retained in the commit trailers:

Co-authored-by: testikun 320479488+testikun@users.noreply.github.com
Co-authored-by: seekskyworld djh1813553759@gmail.com