On MacOS 13.2, the mouse was not recognized by bluetoothcomnnection in the default Logi Options application. If you have the same problem, then the solution is very simple - you need to put Logi Options +, after installation everything worked and it turned out to bin everything as it should :)
Renewed Logitech MX Master π 3 Advanced Wireless Mouse: Exceptional Performance Guaranteed
233 Review
π±οΈ Renewed Logitech M705 Wireless Marathon Mouse: 3-Year Battery & Hyper-Fast Scrolling in Ergonomic Black Design for PC/Laptop with Unifying Receiver
421 Review
π±οΈ Logitech MX Master Wireless Mouse: High-Precision Sensor, Easy-Switch up to 3 devices, Meteorite Black
322 Review
Wireless compact mouse Xiaomi Mi Dual Mode Wireless Mouse Silent Edition, white
174 Review