widget: ship generated type declarations + typed element/events

Integrators had to read the demo to learn the API: the package built via
vite with no .d.ts and no types field, so @bitlogin/widget and
@bitlogin/widget/session resolved to `any`.

Emit declarations from source (tsconfig.types.json -> dist-types,
build:types wired into build) and point the package types/exports
conditions at them, for both the root and the /session entry. Generated,
so they can't drift from the implementation.

Add the type surface integrators actually want:
- HTMLElementTagNameMap["bitlogin-auth"], so querySelector/createElement
  return the typed element.
- Typed addEventListener/removeEventListener overloads (declaration-merged
  interface) for the bitlogin-* events.
- Exported event-detail types and BitLoginEventMap (src/events.ts), matching
  element.ts's dispatchEvent shapes.

Verified with a consumer conformance typecheck (typed detail with no cast,
typed element methods, readCachedSession return type). README gains a
"TypeScript" section.

Addresses the ".d.ts / documented API surface" item of the Tessera
integration feedback (docs/TODO.md).

Co-Authored-By: Claude Opus 4.8 <[email protected]>
Claude-Session: https://claude.ai/code/session_01BXQCvJPA6sVSQ5j8uBd9bB

docs/TODO.md

@@ -416,6 +416,15 @@ how much they cost.
 
 ### Small
 
-- Ship a `.d.ts` (or documented event/method surface) for the element:
-  `getPublicKey`, `signEvent`, `nip44Encrypt/Decrypt`, and the event
-  `detail` shapes. Integrators currently read the demo to learn the API.
+- **[DONE 2026-08-11]** Ship a `.d.ts` (or documented event/method surface) for
+  the element. **Shipped:** the widget now emits type declarations from source
+  (`tsconfig.types.json` → `dist-types/`, wired via `build:types` and the
+  package `types`/`exports` conditions for both `@bitlogin/widget` and
+  `@bitlogin/widget/session`) — zero-drift because they're generated, not
+  hand-written. Added the type surface integrators actually want: a
+  `HTMLElementTagNameMap["bitlogin-auth"]` augmentation (typed
+  `querySelector`/`createElement`), typed `addEventListener` overloads via a
+  declaration-merged interface, and exported event-detail types
+  (`BitLoginLoginEventDetail` etc. + `BitLoginEventMap`) in `src/events.ts`.
+  Verified with a consumer conformance typecheck; README "TypeScript" section
+  added.