feat(web): bound session search pagination

[seekskyworld]

Problem

Adds the pagination slice of #349. A bounded server search needs a stable way to retrieve additional results without loading an unbounded list.

Value

Clients can request 1-100 metadata results at a time with an explicit next offset.

Approach

Add validated offset and limit query parameters to the read-only Session search endpoint and adapter projection. Existing query, archive, and 200-character bounds remain enforced.

Validation

• npx tsc --noEmit
• git diff --check

Impact

• User-visible behavior: paged search responses.
• Model-visible context/tools: none.
• Runtime/lifecycle: read-only projection.
• Persisted config/data: none.
• Compatibility/risk: additive endpoint; transcript indexing remains out of scope.

[tt-a1i]

和 #362 冲突；不要当成 #387

分页上界（1–100、host 拒不安全 offset/limit）是对的，但：

• 和 #362 的 searchSessions 参数个数 / nextOffset vs truncated 不兼容。两份里只留一份，或先 rebase。
• 空 q 返回 200 + []。最后一页长度刚好等于 limit 时会多出一个假 nextOffset。
• 没有测试。
• 这是元数据搜索，不是 #387 的 transcript 正文搜索。

[tt-a1i]

Exact-head review: e202201

[P1] Pagination is applied after the same 500-session UI projection, so it cannot retrieve later canonical results. web/adapter/pi-adapter.ts:314-340 retains at most WEB_MAX_SESSIONS before searchSessions() filters and slices at lines 513-522. Any offset at or beyond 500 is empty, and even earlier pages omit matches that fell outside the newest 500 sessions. The endpoint can still emit a nextOffset as if more canonical search results were reachable.

This breaks the PR goal of stable bounded retrieval without loading an unbounded list. Please paginate a canonical or purpose-built bounded search traversal rather than the snapshot projection, and return continuation evidence derived from that traversal. Add tests with more than 500 sessions, including a unique late match and an offset beyond 500.

Verification boundary: exact-head static boundary analysis; current validation does not exercise data beyond the projection cap.