The screen shot you posted looks like cloud Lightroom, not Lightroom Classic.
If the Photos link says Image > Edit With > Lightroom, that probably sends it to cloud Lightroom, not Lightroom Classic. That would be consistent with the screen shot.
For Photos to send an image directly to Lightroom Classic, in Apple Photos the command in the submenu Image > Edit With would need to say “Edit in Lightroom Classic”, not just Lightroom. But Lightroom Classic is probably not going to be an option, because I don’t think Lightroom Classic provides a direct connection from Apple Photos; I’ve never seen one. But you could get a Photos image to Lightroom Classic in other ways.
The safest way would be to export an image from Photos to a folder, then import that image into Lightroom Classic.
You could also drag an image from Photos and drop it on the Lightroom Classic app icon or window, and Lightroom Classic will offer to import it. However, I wouldn’t recommend this unless you understand the complications. The riskiest way would be if you clicked Add, because that will probably catalog the image at the hidden folder where Apple Photos manages originals and edits. That’s risky because other applications should not modify the hidden Photos folder; that might corrupt the Photos database. If you want to import by drag and drop, at least set the Import dialog box in Lightroom Classic to Copy, and select the folder where that image should be copied outside of Apple Photos for safety.
The basic problem is that both Photos and Lightroom Classic are database-managed apps, but their databases aren’t compatible because their features are too different. But if you export a file from Photos and then import to Lightroom Classic, Photos can render its edits to the image so that when it’s imported into another app like Lightroom Classic, it looks as expected with no further connection to Apple Photos.