If you want Invidious embeds, my recommendation is to use standard Youtube iframe embeds along with a browser plugin like "Privacy Redirect". Unless whoever runs this site wants to let arbitrary iframe embeds be possible, this is probably the best way to acheive the behavior you want (at least for yourself), and bonus, all of the other posts with youtube embeds will now also display an Invidious embed too (just for you).

Invidious is a distributed service, so if you did post a link or embed to one specific server, there is a chance that the embed will just be an error or a bad gateway. yewtu.be doesn't always work, and invidious.io isn't an active instance.

If a youtube embed doesn't work, the average person would probably just troubleshoot it with YouTube, but if an Invidious embed doesn't work, the average person would probably just give up trying to watch the video before they figured out what was wrong, and potentially even, leave a comment below your post complaining about it. This is why it is probably just better to use YouTube embeds. Users who don't like YouTube are already probably using something like Privacy Redirect, and users who don't care will just get the vanilla experience without having any extra issues, and if they do have issues, they are YouTube's responsibility.