There needs to be something going on for it to just pause after 10 seconds. If there is some sort of hardware failure that is causing it and that is what they determined at Apple then it is most likely what is going on. I don’t know what is causing it as there isn’t a lot of information. Have you tried doing a force reboot of the watch? Have you unpaired and paired it again to your phone just to rule out anything software?
Apple isn’t cheating its customers out of anything, you purchased some hardware and it was working, it wasn’t sold to you broken, it didn’t die during the warranty period in which case they would have worked it out with you and not cost you anything extra. If it stopped working and there is some hardware issues, then there is no way to say for sure that it didn’t happen because it wasn’t mistreated or anything. Not saying that is what happened, but there is really not a way to know for sure. On that issue, if it was hardware failure just because it failed, this can happen with all electronics, and not just Apple. This is why extended warranties are offered, you stated that you didn’t purchase AppleCare+, that is a choice that you made and by not protecting it, now when it has failed and it would have been covered now it isn’t. It’s a gamble, it may work out, and it may not. It is sad to hear that you have had this bad experience, and I know the frustration you must feel.
As stated before, I would try to do a force restart and if that doesn’t work then unpair and pair it again to your phone, you can try to restore it from the backup and not and see if that makes a difference as if it is software related then it will remove whatever software setting or issue that it is having. If it still does it, then there is probably hardware related issue and some sensor or something isn’t working and that’s why it is pausing. It never hurts to try first.
If you want to try to force restart it, you aren’t going to lose anything on the watch, just press and hold the side button and Digital Crown until you see the Apple Logo. Once you see the Apple Logo you can release the buttons and allow the watch to continue to load. Once it has booted back up your watch has been successfully restarted.