Repository: yt-dlp
Issue: [Mediasite] Support alternative URL format
Labels: site-enhancement,triage

### DO NOT REMOVE OR SKIP THE ISSUE TEMPLATE

- [X] I understand that I will be **blocked** if I *intentionally* remove or skip any mandatory\* field

### Checklist

- [X] I'm requesting a site-specific feature
- [X] I've verified that I have **updated yt-dlp to nightly or master** ([update instructions](https://github.com/yt-dlp/yt-dlp#update-channels))
- [X] I've checked that all provided URLs are playable in a browser with the same IP and same login details
- [X] I've searched [known issues](https://github.com/yt-dlp/yt-dlp/issues/3766) and the [bugtracker](https://github.com/yt-dlp/yt-dlp/issues?q=) for similar issues **including closed ones**. DO NOT post duplicates
- [X] I've read the [guidelines for opening an issue](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#opening-an-issue)
- [ ] I've read about [sharing account credentials](https://github.com/yt-dlp/yt-dlp/blob/master/CONTRIBUTING.md#are-you-willing-to-share-account-details-if-needed) and I'm willing to share it if required

### Region

_No response_

### Example URLs

https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d
https://uconnhealth.mediasite.com/Mediasite/Channel/medical_grand_rounds/watch/1eeff651adc74b2fb17089ada14b61041d
https://wmich.mediasite.com/Mediasite/Channel/mediasitetrainingvideos/watch/d016dd0c5f384ecfbdb9c8dfc7eefcb21d

Can find more by googling "site:mediasite.com/Mediasite/Channel"

### Provide a description that is worded well enough to be understood

- Each of these URLs are part of a "channel", which is essentially the equivalent of a playlist on Mediasite.
- yt-dlp does not recognise these URLs and falls back to a generic extractor which always fails.
- This can be worked around by right clicking the video → open iframe in new tab
- Another workaround is to convert the URL into a format that yt-dlp detects
  - For example, `https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d` → `https://relaiswebcasting.mediasite.com/mediasite/Play/223f4939531a4a8ca798e0a1dd316e081d`
  - Essentially the format is `urlhost/mediasite/Channel/_ChannelName_/watch/_VideoLocator_` → `urlhost/mediasite/Play/_VideoLocator_`

### Provide verbose output that clearly demonstrates the problem

- [X] Run **your** yt-dlp command with **-vU** flag added (`yt-dlp -vU <your command line>`)
- [ ] If using API, add `'verbose': True` to `YoutubeDL` params instead
- [X] Copy the WHOLE output (starting with `[debug] Command-line config`) and insert it below

### Complete Verbose Output

```shell
debug] Command-line config: ['-vU', 'https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d']
[debug] Encodings: locale UTF-8, fs utf-8, pref UTF-8, out utf-8, error utf-8, screen utf-8
[debug] yt-dlp version nightly@2024.12.15.232913 from yt-dlp/yt-dlp-nightly-builds [d298693b1] (darwin_exe)
[debug] Python 3.12.8 (CPython arm64 64bit) - macOS-15.2-arm64-arm-64bit (OpenSSL 3.0.15 3 Sep 2024)
[debug] exe versions: ffmpeg 7.1 (setts), ffprobe 7.1, rtmpdump 2.4
[debug] Optional libraries: Cryptodome-3.21.0, brotli-1.1.0, certifi-2024.12.14, curl_cffi-0.7.1, mutagen-1.47.0, requests-2.32.3, sqlite3-3.45.3, urllib3-2.2.3, websockets-14.1
[debug] Proxy map: {}
[debug] Request Handlers: urllib, requests, websockets, curl_cffi
[debug] Loaded 1837 extractors
[debug] Fetching release info: https://api.github.com/repos/yt-dlp/yt-dlp-nightly-builds/releases/latest
Latest version: nightly@2024.12.15.232913 from yt-dlp/yt-dlp-nightly-builds
yt-dlp is up to date (nightly@2024.12.15.232913 from yt-dlp/yt-dlp-nightly-builds)
[generic] Extracting URL: https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d
[generic] 223f4939531a4a8ca798e0a1dd316e081d: Downloading webpage
WARNING: [generic] Falling back on generic information extractor
[generic] 223f4939531a4a8ca798e0a1dd316e081d: Extracting information
[debug] Looking for embeds
ERROR: Unsupported URL: https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d
Traceback (most recent call last):
  File "yt_dlp/YoutubeDL.py", line 1624, in wrapper
  File "yt_dlp/YoutubeDL.py", line 1759, in __extract_info
  File "yt_dlp/extractor/common.py", line 742, in extract
  File "yt_dlp/extractor/generic.py", line 2553, in _real_extract
yt_dlp.utils.UnsupportedError: Unsupported URL: https://relaiswebcasting.mediasite.com/mediasite/Channel/aftaamars2012/watch/223f4939531a4a8ca798e0a1dd316e081d
```