Hi @MaPa65,
As per my knowledge, OOTB it is impossible to remove the gear button in SharePoint Server 2019 modern page. Injecting CSS to modern page using SPFx may help in this case but it is not recommended by Microsoft and may break in future if CSS classes get changed in the future. Options under gear button and site contents only show users what they have access to. From my point of view, I don't think this is a good practice in SharePoint.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.