[Feature]: Browser extension: mark clip times on video pages and send to MeTube

Prerequisites

• I have searched existing issues and discussions to ensure this feature hasn't been requested before
• I have read the feature request guidelines in the README
• I understand that MeTube development relies on community contributions and the maintainer is not likely to implement this feature
• I have considered if this feature should be implemented in yt-dlp instead of MeTube (if so, please report to yt-dlp repository)

Feature Description

The Chrome and Firefox extensions linked in the README send a video URL to MeTube for a full download. They do not mark start/end times on the player.

I would like a small extension that:

• on pages with a <video>, lets you set start and end while watching
• sends one clip to MeTube, or several clips, or several clips merged into one file
• uses the batch clip API from PR https://github.com/alexta69/metube/pull/986

This is not meant to replace the existing “send URL” extensions — only to make partial downloads easier.

Needs CORS_ALLOWED_ORIGINS=* on MeTube, same as the other extensions.

Implementation Plan

Yes, I will implement this feature and submit a PR

Additional Context

No response