I think he sounds a little immature - maybe because he is taking behaviour cues from a toddler? It doesn't fit totally with my experience of ADHD, but tbh all kids are different.
6 is a funny age - there is a lot of variance in maturity, and some people do think that boys struggle more, couple with testosterone surges etc.
I wouldn't rush to dx at this point, but I would probably treat him as he were a wee bit younger - ie I would be giving him plenty of warning about leaving places - Ds we are going home in half an hour, Ds we are going home in 10 minutes, Ds we are going home in 5 minutes, Ds, you need to think about putting your toys away in 1 minute - whre did you put your shoes?. Ds please put your toys away and find your shoes etc etc. so that he is expecting the change. No one likes to stop doing the fun stuff and leave, and some kids do struggle more with transitions than others.
I think I would have very firm guidelines. And stick to them. But try to give him lots of advance cues about the behaviour you expect. And I would try to chat (in good moments, generally) about the differences between toddlers and big boys - and I might be telling funny stories about him as a toddler, and trying to get him to show the toddler how to behave - holding him up as a good example - x, can you show y how to go get your shoes on ready to leave? Or ask him to help if he looks receptive, and reward as appropriate.
Usually if kids haven't been dx earlier, they tend to be dx around 7 or 8 (this is really due to the fact that at this point it becomes possible to sort out the difference between immaturity and something else - and schools can no longer ignore differences in the cohort. At 6, it's difficult to work out what behaviours are general immaturity, and which aren't)
If he is doing okay at school, I would try a few things and see how you get on. Tbh, the sad truth is, that even if do get a dx at this point, nothing very much will change - you will still be dealing with the same behaviour issues, and will probably not qualify for any additional support, so you may as well try a few of the techniques, read around, see what makes a difference and get on with it.
And re-evaluate in six months or so. Some of this does does just alter over time. If things get worse, chat to the gp. If they get better, keep doing the good stuff.