Wouldn't you have the same problem with changing workspaces? Sounds like you can't keep track of anything not currently present on the screen, which before the overview was a lot harder to deal with. One thing that could help is to create a "temporary terminal" keybinding to launch in floating mode so you'll never forget to close it. Or create a focus-or-launch bind that switches to an existing terminal (tools like Nirius can help minimize scripting). The other thing that may help is adjusting your struts so you can see that windows exist to the left or the right. More of general workflow tip than one related to just terminals.
Yes and no; the difference with workspace is that I was limited to 0-9 with my old wm, so at some point I'd just run out of space and had to close some windows. (well, that, and X11 is apparently limited to 256 clients by default and I never changed that; but I rarely hit that limit :P)
I do have some struts on the side, but I'm basically always juggling with at least 4 or 5 tasks so I always have things open; (I'm not using any right now but I do like the "quake terminals" temporary term styles... But for the same reason it's not always appropriate -- if I didn't close the term, it's because I wasn't done with it and mean to get back to it...)
I started using niri before the overview, I think that could help if I get used to it. But better than overview, what I'd want is something always visible like some horizontal scrollbar indicator to remind me there's e.g. more than 3 windows hidden or something. That might be possible to do with waybar and a bit of glue parsing the windows list...
The latest release exposes information about windows list and positions via API. Someone can write a widget for waybar or any other bar.
Oh! That didn't exist a few months ago, I need to update and do this then :D