I've just held onto random ones I've run across, e.g. itags have been reasonably popular for a while: https://devices.esphome.io/devices/ble_itag and during BLE / IoT bursts of hype random things are sometimes handed out for free at and around events (not often programmable, but that's usually fine - they broadcast a unique ID when powered / when pressed, that's all you really need).
I also have one of these because I get a lot of use out of newsblur and figured I'd support the maker (I don't actually recommend it because it's pricy and not very well supported... but it's functional and flexible): https://www.kickstarter.com/projects/samuelclay/turn-touch-b...
IKEA Symfonisk is 50mm round but it has press and rotate. I was actually thinking of Aqara WXKG11LM. It's 45mm square with round corners, but only 12mm thick.
Otherwise you can look at the Picoclick. It's 18x22m (height unknown) with no enclosure, with is 20.6x22.6mm and 11.6mm tall. Smaller than that is probably hard. I have never seen the Picoclick in stock, so you might have to build it yourself. It seems like a neat product, it's too bad the creator doesn't make it available.
Background:
I’ve been trying to find something like that but everything I look at is Smart Home related and bigger than needed.
The smallest BLE button that I did find is part of a cheap China Gadget used to scroll tiktok/social media. Like this https://www.amazon.com/Bluetooth-Control-Photograph-Scrollin...
Unfortunately I couldn’t figure out if it’s hackable or not