When will the mouse/trackpad 3 second cursor lag be fixed on Catalina?

Catalina is no longer receiving security updates. Except for the random one-off situations where there might be a security fix that happens out of the blue, it is unlikely to receive anymore.

When you look at this page:

Apple security releases - Apple Support

you'll see every annual named upgrade, is followed with up to 9 updates and an array of security updates for up to two years after the upgrade is replaced by a new upgrade.

The mouse lag issues you are getting can happen because of numerous background applications that are known to create issues

• USB low power mode after Energy Saver is woken from. Any external USB device may not get sufficient power unless it has its own power source or is attached to a hub with a separate power source. Lag in communication to such devices persists after you open the screen lid of a laptop and/or wake from sleep until such time you restart or shut down and power back up the computer.
• iCloud Synchronization. The more you attempt to sync with iCloud or any other cloud service the more lagging can happen. The internet is asynchronous communication. This means data coming off the internet to your computer (download) is faster than data going to the internet (upload). The only exception is people with dedicated fiberoptic lines direct to their computer.
• Time machine. Runs as an automatic backup unless you turn it off in Apple menu -> System Preferences. In the same panel, you can add a menubar item to manually restart the backup when you don't use the computer.
• System optimizers. A wide variety of optimizers from MacPaw and Zeobit have lured people into downloading them who believe Macs need optimization. They don't. These optimizers including MacKeeper and Advanced Mac Cleaner are so notorious most Mac support consider them malware. If you see them in your Applications folder, download http://www.reggieashworth.com/appdelete.html and boot into safe mode (holding the shift key), and drag their application over AppDelete when launched. Manually deleting just the application may still leave behind launchservice background apps, which can be revealed with Etrecheck:

Etrecheck - the handy reporting tool for … - Apple Community

and removed in safe mode with Devon Technologies EasyFind:

https://www.devontechnologies.com/apps/freeware

• Hard drive space. Generally speaking your boot drive should not exceed 85% capacity. This amount when exceeded can create a lag while the computer tries to find more space for swap files.

• Spotlight reindexing - if Spotlight reindexing gets slowed, it could cause a lag. Try rebuilding your index:

Rebuild the Spotlight index on your Mac - Apple Support

Check the health of the hard drive with http://www.binaryfruit.com/ DriveDX. A slowly aging hard drive could potentially have lag issues as well.