That “Failed to personalize the software update” message is a documented macOS installation error.
Since this started after you changed your modem, I would first try the update over a completely different Internet connection, such as a phone hotspot or another network connection.
Apple notes that macOS needs a stable Internet connection to download the installer and obtain firmware and other information specific to the Mac.
If you use a VPN, firewall, or proxy, also check that it is not blocking communication with Apple. Apple: If an error occurred while updating or installing macOS
Also check that you have enough free storage.
If the update still fails, try installing macOS from Recovery.
If you want to try Software Update again first, Apple also recommends trying Safe Mode.
If the problem continues, use Disk Utility from Recovery to check and repair the startup disk.
Because yours is an M2 Pro MacBook Pro, Apple says that a persistent installation problem may, in rare cases, require a firmware Revive or Restore.
Revive is the first option because it does not erase the Mac.
Restore is used if Revive does not resolve the problem and does erase the Mac. Apple: How to revive or restore Mac firmware
I wouldn't erase the Mac yourself at this point. If the error remains after these steps,
Apple Support or an Apple Store can determine whether a firmware Revive or another service procedure is appropriate.
Have the computer evaluated by the Professionals who have the Special Hardware Software and Expertise to diagnose the issue and offer possible solutions
Make an Appointment at the Apple Genius Bar or call 1 800 MyApple and have them evaluate the computer
Other location Call Centres
Contact Apple for support and service