the timer has no idea if it was triggered during last boot. It only has the context of “this” boot, so it will do it right after a reboot and set a timer to start the service again after a week of uptime.
So if you reboot every day, it will trigger the service every day, even though you set it to weekly in the timer.
So it’s up to your .service file to determine if it has been run this week or not.