I had One that had acted like yours and then stopped working completely shortly after that. I think it was older than 2021 though, not sure, but probably the same model. I ordered another one and interchanged parts and it was not the battery. It seems like it is the switch or at least it is in the head where the main electronics are located. It's not official, but contacting cs to get it sent in and checked out would be my next step. You might want to consider that route. I hope this was helpful. P.S. The reason I ordered a second one first is because it is my favorite small-size EDC and I figured that way would be the least number of days without one.
I've had my perun mini turn off / not come one once. The body was just barely loose (like not snug) to the head. make sure its tight.