I think this is the issue, in addition to the fact we imitate user input on the textarea on this type of addition to avoid losing the undo history.
I believe it can be “solved” with a spellcheck="false" on the element, but it has an obvious downside.
What’s causing the issue is the inconsistent quotation, it would work if it had the same style of quotes on both ends – any of these sets can be used:
It’s weird that only the second quotation mark got converted when quoting though, both sides get converted if the same BBCode is typed manually.