From the video when you press it's hard to say. Tested now and swimming change is pretty instant under 1s.. trail run change is 1-2s and I'm blaming the maps..
I'm again pointing towards the maps update, for me that caused lagging in the running and walking activity...
Try connecting the watch to a computer, create a subfolder 'backup_map' in the GARMIN folder and move the gmapdem.img and gmapdem.gma files in there. Reboot and try again...
I don't really miss the dem (elevation data) file, not sure what exactly it's used for to be honest. Maps still work fine as in routing,points around me, etc.
But this made the watch usable for me again at least, worth a shot.
(I tried reinstalling maps a few times but the issue maintained, tried it in various ways... fed up with it as it's very time consuming and frustrating so this is a workaround I can at least live with for now)
