I haven't looked for the smallest Arduino. I have a ESP8266 waiting for me to experiment with, but I simply have not gotten to it yet.
However, the ESP8266 models can come with a few challenges (not terribly complicated) to make them run native Arudino code.

I did find this article discussion a few options. I do not know how neutral this list is of course.

Personally, I'd probably use an Arduino Nano, but the list shows a few seemingly good options.
I'd probably go for the "Seeeduino XIAO", as it does not seem to be needing any "extras" (some boards are kept small, by making certain parts (like the USb connector) external. This one does not seem to do that and it is tiny.

I did see them listed at Amazon (USA and DE) for a little more than $20 for 3 of them. Or get them for $5 at Robotshop (link).

On that note though: I've not tested this one, and I do from experience that some not original Arduino products can come with challenges (like needing a special driver etc).
I did however not find any negative reviews either.

Any suggestions welcome

Thanks Richard