P: Open With should launch Lightroom Classic in Import mode.

Applications need to register with the operating system as being capable of opening certain file types. This system is a holdover from the time of the fishbowl macs and a time when Macs did not use file name extensions to identify file types and this system is woefully anachronistic and something Apple should have fixed over a decade ago. Classic is far from the only app and file type where this mechanism doesn't work well (try getting pdfs to open consistently in the right app (i.e. not acrobat even if it is installed) for example) and while Adobe could fix this by doing the correct registrations with the OS, just dragging and dropping works much better than open with. Adobe should still fix it though.

This may seem like a minor issue, but it is a constant annoyance.  When I right-click on a image file, the MacOs "open with" context menu includes Adobe Lightroom, Adobe Photoshop, and a host of other options, but NOT "Adobe Lightroom Classic.app" And if I click "Always Open With" there is no change in the behavior.  So every time I want to open an image file in Lightroom Classic, I have to click "other" then fish around in the submenu of Lightroom Classic in order to find Lightroom Classic.app. Is there any way that Lightroom Classic can be included in the "open with" menu, like all the other Adobe products?

Open With exists as an option on Montery (12.6), so this is likely an issue with OS 13 beta/bug and nothing we can help you with as it's a beta OS. That said, what Bob wrote is key; you don't open, you import. But Open With is an option today on a released OS. 

You don't "Open" images in LrC, you Import them.  Lightroom Opens catalogs.  If you have an image or images selected than just drag the photos to LrC while in Library view or to the LrC icon in the Dock in any view.

Agreed, it would be convenient to have Finder's Open With Lightroom Classic behave similarly to Open With Lightroom, opening the Import window with the photo or photos checked.  Unfortunately, Lightroom Classic doesn't provide that. 

However, on Mac, you can drag photos from Finder to the LrC icon in the Dock, and that will do the same thing, opening the Import window with those photos selected.

On both Mac and Windows, if Lightroom Classic is open in Library, you can drag photos from Finder / File Explorer to the center of the Library window, and the Import window will open with those photos selected.

And on both platforms, if Lighroom Classic is open in Library but minimized to the Dock, you can drag the photos from Finder / File Explorer to the LrC icon in the Dock, hover over the icon until Lightroom unminimizes, and then drag the photos to the center of the Library window. (On Mac, you have to haver, wait until a thumbnail of Lightroom appears above the dock, then hover over that.)