feat(webui): add the shared typed client and state synchronization

[inureyes]

Parent / dependencies

Parent: #1834. Depends on #1835, #1836. Build against canonical fixtures; backend endpoint implementations are integrated later, not redefined here.

Ownership

Own webui/src/api/, generated DTO integration, webui/src/state/, authentication state, query/cache/event infrastructure and deterministic transport tests. Feature pages must not create private fetch wrappers, timers, auth storage or model-state caches.

Required behavior

• Same-origin relative URLs from the server-provided validated API base; reject externally supplied backend URLs. Encode query parameters safely, distinguish catalog opaque ID from actual inference model string and attach autoload=false for model-scoped observation/inference. Bootstrap validates schema version and shows an actionable mismatch screen.
• Bearer credential is memory-only, submitted through a login view; never URL/sessionStorage/localStorage/IndexedDB. Abort requests, streams and pending retries on logout/401. A 403 is forbidden, not a login loop. Distinguish server offline, empty, partial, stale and unauthorized states; show last successful update age.
• Use fetch-based SSE for Authorization support, including model lifecycle and chat streams; implement incremental UTF-8 decoding, CRLF/multiline frames, comments/keepalives, split JSON, finite buffers and cleanup. Do not use EventSource with token query strings.
• One shared model/catalog cache and event reducer with instance/revision checks, duplicate/out-of-order handling, snapshot fence and reset. Reconnect has jittered exponential backoff; no action auto-retry unless safely tied to the same idempotency key. Connection loss while a POST outcome is unknown triggers operation reconciliation, not a second load/download.
• One non-overlapping fallback polling loop (2 seconds visible/30 hidden), pause unnecessary views, coalesce refreshes and cancel work on teardown/model switch. Observe without influencing LRU or autoload. Use typed nullable metrics and error codes; do not coerce failures to zero.

Acceptance criteria

• Unit tests fuzz/split SSE at byte boundaries, including multibyte CJK and CRLF, [DONE], oversized frame, midstream failure and abort. Preserve distinct reasoning/content/tool/usage frames.
• Fake-clock tests cover lag/reset/restart, obsolete model response, reconnect unknown POST, tab visibility, logout and mount/unmount; connection/timer counts return to baseline and requests never overlap.
• Shared fixtures compile without any and validate runtime JSON at the boundary; seeded secrets never reach persisted stores, logs, errors or exported diagnostics.
• Expose documented page hooks/actions so Models, Chat, Activity and Settings integrate without changing the state authority or auth design.