I was able to get rid of the button like this:
Edit: This works instantly, but the key is recreated after reboot. You can prevent this by denying write permissions to the key:
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In the left pane, right-click on the OneDrive key and then click Permissions. In the dialog click Advanced.
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Add a new access entry for user Everyone of type Deny. Under Advanced Permissions just select Set Value.
Only other solution for me was uninstalling OneDrive. The option 1 by @cam-ashton doesn't seem to work with latest Windows 11 (23H2) anymore.
