Note that you can use systemctl list-timers to see all active timers including when they will next run and when they last ran. This is very useful for seeing if you have set things up correctly.

There are multiple ways to do this as well. You can do

OnCalendar=Sun 03:00
Persistent=true

To run every Sunday at 3am. And will run immediately when activated if the last time was skipped due to the system being off. Think that is the closest to your cron job.

You can also

OnCalendar=weekly
Persistent=true

If you don't care when it will run. This is equivalent to Mon *-*-* 00:00:00.

OnCalendar is calendar-based, not interval-based.

Use a monotonic timer with OnUnitActiveSec=7d plus Persistent=true . This is not quite the same as your cron, because it can drift the day of ghe weak.

And no, it does not reset just because you reboot.

Would something like

OnCalendar=Wed *-*-* 03:00:00

Technically not the same as every 7 days, instead it's every Wednesday.

This might interest you. https://crontab.guru/

Check the man pages, starting with man systemd.time