Which BT game controllers work with Vero4K+ built-in BT hardware (no extra USB dongle)?

So far I considered /tried:

-xbox360: not BT, needs extra dongle
-ps dualshock4: pairs, but mappings not the best and need to connect manually after reboot
-xbox model 1914 (year 2020 for xbox series x and s): BT pairing and connecting seem to work, but the controller ignored that and does not work on the Vero4K+

So now I am looking for a not too expensive but reasonably good game controller that I may connect to Vero4K+ built-in BT hardware without the need for an extra dongle.

does such a thing exist? if you are using one, step forward and give details on the manufacturer and model (preferrably something that may still be bought on mainstream channels like Amzn).