I would start off by making sure nothing is blocking the sensor on the bottom of the mouse, compressed air works great for dusting.
You could also try resetting Mac’s BlueTooth module by doing the following.
Press and hold the Option + Shift keys together on your keyboard.
While pressing the keys, click the Bluetooth icon in the top-right corner of your Mac’s menu bar.
Then click the Reset the Bluetooth module option. Then follow the onscreen instructions.
Lastly, you could try the following.
Reset your Apple mouse
Press and hold down the Shift + Option key; then on your top menu bar, select the Bluetooth icon.
Press Debug > Remove All Devices.
Repeat step 1, this time selecting Reset the Bluetooth Module.
Now try to pair your mouse again.
Let us know how it goes.