1. Set AirDrop to Contacts Only or No One on both Macs: Wi‑Fi stutters when AirDrop is set to Everyone.

  2. Choose a lower quality in the display’s Quality menu, or choose Test Connection… there for a new recommendation.

  3. Use Ethernet, or a cable between the two Macs. A Thunderbolt cable gives the lossless picture; any cable avoids the stalls of a radio.

Check Smoothness… in Settings › Display measures what the display shows and suggests what to try. Check Smoothness