If you are suing a DIRECT cable connection, Mac to display without a Dock, there is nothing in the display-chain that is slowing performance.
Mouse cursor-position updates are performed by the main CPU at low priority in the background. if you are seeing poor responsiveness and slow mouse tracking, it is likely cause by added software that is poisoning performance on your Mac.
Poisoning Computer Performance:
By far the easiest way to cause poor performance, instability, overheating and crashing is to install ANY third-party speeder-uppers, Cleaners, Optimizers, or Virus scanners. or a VPN that you installed yourself.
The idea that a third party, with no special knowledge of the inner workings of MacOS, can somehow find a simple way to protect your computer — that is not already being done by MacOS itself — suggests that the MacOS developers are somehow "holding out on you". That is absurd.
You should remove any and all (other than Apple built-in) virus scanners, speeder uppers, optimizers, cleaners, App deleters or VPN packages you installed yourself, or anything of that ilk.
Third-party file Sync-ers such as DropBox, BackBlaze, OneDrive, or GoogleDrive can ruin performance, but are not inherently dangerous.
Effective defenses against malware and ot… - Apple Community
Effective defenses against malware and ot… - Apple Community
To determine whether added software is the problem, run in Safe Mode, where no third-party items are loaded.
"Works in Safe Mode, Fails in regular mode" implies, "it's something you added."