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
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...
The tiktok ring on the other hand manages to put a simple button, bluetooth, battery and usb port all into a package of roughly 6x10x4mm
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.