Embedding text containing a tag doesn’t actually apply the tag. Here’s a request for a toggle that allows that type of functionality: Toggle to let embeds share tags/links
Although I don’t quite know how to do it, I imagine that if you standardized where you added the tags, etc, it would be possible to create a Templater script to do this.
I was trying to figure out how to do something similar and received some hopeful suggestions, but no Templater solution. On the other hand, I was able to create a little AutoHotKey macros to save some time. Here’s the link if you want to check it out: Copy text and block link to clipboard
You might consider checking out Note Refactor plugin, although it probably will be unable to accomplish what you want.
Good luck!