There is very little technical information in the original description to begin meaningful troubleshooting.
The fact that the Magic Mouse stopped working after upgrading to macOS 27.0 is useful, but it does not by itself identify the cause.
The fact that Apple Support was unable to provide a solution also does not establish whether the problem is caused by macOS 27, Bluetooth, pairing, the mouse, or another factor.
First, turn the Magic Mouse off and on again, making sure the green indicator is visible.
Make sure Bluetooth is enabled on the Mac, then connect the mouse directly to the MacBook Pro with its USB-C cable.
Leave it connected for about a minute.
Apple states that this should pair the mouse with the Mac and charge its battery. The cable is used for pairing and charging; it must be disconnected for the Magic Mouse to be used wirelessly. Apple's Magic Mouse connection troubleshooting
If it still does not work, open System Settings >> Bluetooth and check whether the Magic Mouse appears and whether it is connected.
If Bluetooth cannot be turned on, Apple recommends restarting the Mac and trying again.
If the mouse appears but does not connect or remain connected, possible wireless interference can also be considered.
Resolve Wi-Fi and Bluetooth issues caused by wireless interference
The most useful additional information is whether the Magic Mouse appears in Bluetooth, whether it pairs when connected by USB-C, whether it works after the cable is disconnected, and whether another Bluetooth mouse works with the MacBook Pro.
Those observations would help determine what to investigate next.
If the Mac recognizes the Magic Mouse, its firmware version can be checked in System Information >> Bluetooth.
Apple documents firmware updates for supported rechargeable Magic accessories when they are connected and charging while the Mac is awake. Apple's Magic accessory firmware information
Apple's current specifications list the USB-C Magic Mouse as requiring macOS 15.1 or later, so macOS 27 falls within Apple's stated system requirements.
This does not establish the cause of the reported problem. Magic Mouse (USB-C) technical specifications — Apple Support
If the mouse remains unusable after these checks, the next step would be to document the Bluetooth status, USB-C pairing behaviour, and results with another mouse and provide those specific observations to Apple Support. That gives Apple more concrete information than simply reporting that the mouse stopped working after the macOS 27 upgrade.
If you can't connect your Magic Keyboard, Magic Mouse, or Magic Trackpad to your Mac — Apple Support