Just press the video button and there you go! For mobile, hit the attachment button, click add video, click add, record your video.
You get:
Automatic captions
Timestamps
Playback speed
Quality up to full HD
Thumbnail picker
Recording and uploading videos from the Skool mobile app
I go deeper into all of this in the attached video.
Update:
You can now upload videos to DMs
You can now add videos to your about page
The file size limit is 30GB (except for DMs where it's 1GB)
The video upload speeds feel pretty good (although some people say that other video hosts are faster).