Feature: Media Session API integration (OS media controls + hardware keys reflect playbackRate)

[chirag127]

Feature request: Media Session API integration for OS media controls

When VSC changes video.playbackRate, the browser's Media Session (surfaced by Windows 11 SMTC flyout, macOS Now Playing, ChromeOS/Android media notifications) does not reflect the new rate. Reported position/duration in those OS controls drifts because the OS assumes 1.0×.

Additionally, hardware media keys and OS-level seek buttons currently route to the page's own handlers only — VSC's advance/rewind/faster/slower shortcuts aren't exposed to Media Session, so users can't drive VSC from a headset button, keyboard media keys, or the SMTC flyout.

Proposed:

1. When VSC updates playbackRate on the active video, call navigator.mediaSession.setPositionState({ duration, position, playbackRate }) on the same element.
2. Register setActionHandler('seekforward' | 'seekbackward') mapped to the existing advance / rewind actions (opt-in setting, off by default to avoid clobbering site handlers).

MDN refs: Media Session API, setPositionState.

Thanks for the great work on Video Speed Controller!