What do you mean by embed codes? It has nothing to do with the format to embed a video. The CMS plugin handles embedding.

from your answer, I get that uploading is still needed. So you’re talking about sharing a video with an embed code that that seconds, vs. a whole technical operation that probably takes several dozen minutes.

Uploading a video to your own site gives you control over the information you posses. Otherwise it is under the other site’s control. It need not be a very technical operation. I don’t know if there is an easy way to do it. That is just a question of hiring the correct person to do it. I think what Bob suggests is a good suggestion. But there could be other options. You could also upload videos to a site that is not yours and link or embed the remote video. But the idea is to have sovereignty over your own resources. If you want to do that anyway, use https://wiki.mediagoblin.org/Live_instances

no, open formats, at least until the last time I tried, had no embed codes, you had to download them, re-upload them, which was too time-consuming, so they were must less shareable. Has that situation changed ?

You can embed anything in a web page.

I do not see what your problem was at the time. But if you mean that Youtube was not available to view on a free format, it has changed. You can now see Youtube in webm; which is a free format. But it is not the default https://www.youtube.com/html5 . Additionally, Youtube has Javascript that may be executed in your browser without you knowing what it does in your machine. I call that a virus.

The current problem that we noticed with the video in this post is that it was taken down. We do not know if it was censored or the user took it down. The best is to upload to your own site and have the alternate link to the other site. Then you can publish it on a free format. The alternative to hosting it yourself (which is the best) is to upload it to archive.org on a free format. There still remains the issue that in order to embed a video some plugins use non-free software and have heavy surveillance code. You should choose a plugin to embed videos that avoids that.