Anker or UE Wonderboom maybe?

JBL Charge 5, or basically any JBL spesker.

You press one button to turn it on, you don’t hold it or anything, just one press, and like all Bluetooth devices, it connects to the last device using it.

I have a Bose Soundlink Micro Bluetooth speaker that goes into a low energy standby anytime it’s not being used. I am able to connect to it and start playing music without pressing any buttons on the speaker. Sounds like what you are looking for. I imagine all their Soundlink speakers have BTLE (and they can be grouped).