that's an interesting issue. I have never even tried to add a self-hosted video to a forum post, but since you mentioned it now I had a look is this is even possible.
There are a number of discussions about this
on the PHPBB support forum but no clear-cut answer either way. It should in essence be doable, but I'm afraid that the results wouldn't be all that great: it requires custom BBcodes for with the width and height need to be specified in each case; and I'm also concerned that there might be issues with accessibility of the video file.
For instance, the one you uploaded is on iCloud, and it says there that the shared link will expire on July 12 (which might not be what you want).
We could also upload the video to the host. In individual cases that should be fine, as long as it's not going to be gigabyte amounts - but I just tried that, and I can't get it to work that way either, though it might work to a degree if we would resort to some serious hacking
I also tried just attaching it to a post like you can do with am image. But that doesn't work either, because the board complains that it doesn't recognise the file format.
All in all, I think it is much easier to upload the video to a regular video sharing service like Youtube (or whatever else: Vimeo, Dailymotion - the [media] tag of the forum (that you tried to use as well for this video) supports more than 120 different different ones. Here's the complete list: https://s9etextformatter.readthedocs.io ... bed/Sites/
Note that if you don't want a video uploaded to, for instance, Youtube to be visible to the whole world: on Youtube you can mark your video as "unlisted". That way, the video will never show up in any searches, even though it is not truly restricted (which you can also do, it's just a bit more work). If you then put that video link here, it should show up fine.
Let me know if I can help you with anything!