Got the Mother-in-law a “Roma City Walker Lightweight Folding Rollator 4 Wheel Walking Aid” a few years ago and it folds down very small but is very sturdy.
The OH took her to Venice with it and managed to carry it up and down the dozens and dozens of stairs around the city and it was small enough to go in with the hand luggage in the overhead compartments.
I think we paid less than £100 but everything seems to have gone up in price lately.