I think a sensible ”solution” might be for OS vendors (usually not that different from browser vendors) to continuously monitor the clipboard just like anti-vir

I think a sensible ”solution” might be for OS vendors (usually not that different from browser vendors) to continuously monitor the clipboard just like anti-virus software is monitoring the file system for viruses. And block access (or condition it with hard warning modal) on pasting flagged text. Possibly allow pasting to same site without check.