My original idea was to leave the folding gutter for headings and tables. Below is an example:

However, I just realize that there is no conflict with additional gutters for templates spanning multiple lines.

For now, how about simply hiding the folding tooltip when typing?

In T367256#9883119, @Bhsd wrote:

For now, how about simply hiding the folding tooltip when typing?

In discussion with @MusikAnimal, we think that making the tooltip semi-transparent by default and fully visible on hover is a good idea, in the short term. It should be tracked in a separate task, though.

Hiding the tooltip or making semi-transparent sounds like a fine improvement. I'm leaning more towards hiding, because semi-transparent could look weird or still be distracting. No one wants to collapse the template while typing anyway, so it makes sense to use a keyup debouncer or whatever so that the tooltip only shows when the user stops typing. Maybe we should both hide until typing stops, and have it be semi-transparent until the user hovers over the tooltip. I say this because one might stop typing to read what you just wrote, and it'd be jarring to have the tooltip suddenly obstruct your view.

In T367256#9883014, @Bhsd wrote:

However, I just realize that there is no conflict with additional gutters for templates spanning multiple lines.

Yeah, if we could get it working for infoboxes etc. that'd be awesome! So we wouldn't show a fold toggle in the gutter for inline templates, right? I think that would be fine. I'd worry about the logic being too fragile… but I suppose for gutter vs. tooltip it's simply a matter of seeing if the first token is a template bracket and that there's a newline somewhere before the closing bracket.