It can be confusing, as there are at least two main updates for each watch:
Wear OS - all watches should get the same one - this tends to be done via the Play store.
Watch software - depends on manufacturer as to how often this is done. Your watch should be on the June 30th update (easiest way to check is if you have the new Suunto tiles). If not got into setttings, system, about (in this area you can also see all your software versions - click on versions to see them - then swipe back to go back to about), scroll down to second last option - system updates and press on it. Watch will check for latest watch update.
And some like Suunto have a 3rd one - the suunto app (the app on the watch is updated in watch software, but good idea to keep phone updated too) on the phone which can be done via the play store ont the phone.
Best optin is to set play store to auto update, and at least this way 1) and all your apps will be taken care of when you put your phone on the charger, plus it will be faster as wifi comes on when on charger, which is often quicker then trying to update via bluetooth connection.
