Laggy external monitor with macbook pro m4 pro

If your MacBook Pro has a M4 Pro chip, it is capable of driving two external monitors in a hardware-supported way.

Is there some reason that you are using AirPlay instead of a hardware connection? An AirPlay connection over Wi-Fi will be competing with anything else that is taking Wi-Fi bandwidth, and will be subject to radio interference in all of the ways that Wi-Fi networking can be. It's also being driven by software – not by dedicated hardware designed to keep a steady stream of video data flowing even when your Mac's processor is busy.

With regards to the wireless mouse, is this

• An Apple Magic Mouse (of some flavor) that uses Bluetooth?
• A third-party mouse that uses Bluetooth?
• A third-party device where the mouse has a proprietary wireless connection to a USB receiver (that you plug into the computer)?

in round numbers:

1080p data stream at 60 Hz over DisplayPort CABLE uses a steady 5 to 8 G bits/secs.

the best "regular" Wi-Fi can support about a 1 Gigabit/sec connection, with some pauses and interruptions.

if you want a "snappy" display, use a Cable. it beats AirPlay in responsivenss every time!

if you have to buy new cables, lengths one meter or shorter will be much more useful in the long run.

if you have to buy an HDMI cable, "PREMiUM" or "ULTRA" cable are the most reliable.

how have you connected the external monitor to the computer ?

please mention every item in the chain: every cable adapter and dock.