fix(core): decouple data sending state from subscriptions

[fatihcvs]

setupDataMessageHandler().send() throws before publishing if nobody subscribed to isSendingObservable, because its stored subscriber is still undefined. Subscribing more than once also overwrites that subscriber, so only the latest observer sees sending-state changes.

Use a BehaviorSubject for the shared sending state and expose it as an Observable<boolean>. Sending no longer requires a state subscription, all observers receive updates, and a subscriber joining during a send receives the current state. The existing publish-error propagation and finally reset are preserved.

Validation:

• Three regressions fail before and pass after: send without a subscriber; multiple/late subscribers with one unsubscribing; state reset and original error propagation on publish failure.
• Tests use a real SDK Room with publishData stubbed to control completion/rejection; no server connection is made.
• 121 core/react/styles tests pass; pnpm build:react, core lint (14 existing warnings), pnpm format:check, and React API check pass. The generated sending-state return type remains Observable<boolean>.

Includes a core patch changeset. Developed and verified with OpenAI Codex assistance.

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[changeset-bot]

🦋 Changeset detected

Latest commit: 43bc945

The changes in this PR will be included in the next version bump.

This PR includes changesets to release 7 packages

Name	Type
@livekit/components-core	Patch
@livekit/components-react	Patch
@livekit/agents-ui	Patch
@livekit/component-example-next	Patch
@livekit/components-js-docs	Patch
@livekit/component-docs-storybook	Patch
@livekit/components-docs-gen	Patch

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