Hi waynecar and thanks for posting.
Quoting waynecar,
ON Windows 11 25H2, Build 26.200.8037, the Taskbar will not auto unhide at times. I reported this to Windows 11 Support and they did not know of any such issue but noted it could be because of Start11 (now version 2.6) since it has a Taskbar hide setting. After I just did a Windows Repair the Task bar unhide issue was not resolved. The last test was with setting the Windows Taskbar to hide in Windows 11. I have the same problem when the hide feature is set using Start11 and the setting in Windows is not set.
End of waynecar's quote
This is not reproducing for me in the latest Start11 release (2.74 at this time). Any use of Start11's autohide is "unhiding" for me as expected.
However, since your original post, improvements have been implemented that relate to the Taskbar. You might find resolution with the current (2.74) version.
No, I want to try not using Start11 to control the Taskbar of course to try to stop the Taskbar unhide issue from occurring. I understand Windows 11 does not have a Taskbar unhide issue unless a third party app is interfering with its operation.
End of waynecar's quote
While it could be true that "Windows 11 does not have a Taskbar unhide issue...", the Start11 Enhanced Taskbar does (by design) impact the functionality of the Taskbar. By enabling the Start11 autohide mode specifically (instead of from Windows), you are enabling an autohide function that Start11 supports. This is displayed clearly in the app:

Please try doing this as requested, in the latest version to confirm if it resolves the issue.
If it does not, make sure to restart explorer and try again. If it continues to be an issue, more specific reproduction information may help. At this point detailed explanation of the exact steps to reproduce the issue (with a video upload if possible) would be helpful.
We would also request that include clarification of your taskbar alignment (default bottom/left/right/top alignment), your monitor setup, display configuration, and other specific settings you may have enabled for your Taskbar and in the app.
A good way to check if a setting is contributing to this would be by saving a backup and restoring your settings to their defaults:
https://support.stardock.com/space/SHC/1995702300/Start11+v2+UI:+Settings+backup
Please let us know if this helps, and if we may be of further assistance.
Best regards,
Adam McGuinness
Stardock Support Specialist