This is the current state-of-the-art for Obsidian as far as I am aware: Clip selection to Obsidian
You have to install a special extension for Obsidian mentioned at the start of the thread, then install one of the snippets posted in the thread: this one
I will look into making this an “official” PopClip extension soon since it seems to be established as working well. I had not done it yet because it requires that extra install step, but I guess it’s not too big a hurdle.