@alexwiw There are no SharePoint out of the box ways available to hide the Share button from SharePoint site modern experience.
You may have to use custom solution like SPFx and custom CSS. If you want to hide it from specific/single site page use modern script editor and If you want to hide it from all modern pages, use SPFx application customizer.
Check below threads for more information:
- How can I include the same JS and CSS files on multiple SharePoint Modern Page?
- Hiding Office 365 Ribbon in SharePoint
Note: DOM manipulation & CSS customizations are not recommended by Microsoft and some of your customization may break if Microsoft changes HTML element id/classes in new release updates.
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