Before wipe and install of an older operating system, try these things:
- Boot into Safe Mode. Is the problem gone? If it is, then something installed is to blame.
- Create a new user to test if the behavior occurs when you log out and log back in as the new user. If the new user is not affected, that would point to something in your user setup.
- To get more information for various MacOS experts reading here, download and run Etrecheck and post its report here with the additional text button below. https://discussions.apple.com/docs/DOC-250000211
When you upgrade to Tahoe, there are multiple reboots with the screen going blank for a few minutes each time. During some of these restarts, firmware updates MAY be installed. Those firmware updates MAY be incompatible with older versions of MacOS. If you erase/reformat and install an older MacOS and encounter this roadblock, to get around this requires a special configurator process using another Mac, something that might be best done by an Apple Authorized Service Provider. Just pointing this out to encourage you to thoroughly pursue one those three options above before embarking on a rollback to an earlier system.
By the way, you would need a backup done before the Tahoe upgrade to recover your pre-Tahoe Mac as it was. If you only have backups post-Tahoe, that won't work to restore a working computer because some of the Tahoe upgrade modifies various Apple apps and their associated files/formats.
One last point: scores (millions if not billions) of users have upgraded to Tahoe and NOT seen this jumping cursor issue, so I am fairly confident that something installed is causing this. Etrecheck might help identify the culprit.