My old house had the same glossy oil paint on every door. I tried a citrus based stripper from the hardware store, the kind in the yellow can. It took three coats and a lot of scraping with a plastic putty knife, but it got down to the wood without a huge mess. Just make sure you let it sit long enough to really bubble up. After that, a light sanding was all it needed before the new paint stuck perfectly.

Yeah, I used to just blame myself for not reading the fine print, but hearing this from you and @eva_rivera shows it's a real design flaw. Why hide the thing most people need to do every day? If paying a person is a common task, that button should be front and center, not a secret menu item. It's not about exploring more, it's about them making the right choice obvious. They basically built a door but put the handle where nobody can find it.

Oh man I've been there lol. I did the exact same thing with a cheese sauce last week, total glue. What saved it was taking it off the heat and whisking in a splash of milk really slow, like a tiny bit at a time. It came back together way better than I thought it would. Gotta go super slow with that thickener.