edge 1040 solar (25.19) verbindet sich nicht mit MacOS(14.6.1) oder mit Basecamp(4.8.12).

What version are you on exactly? You're saying your not part of the beta programme, but 25.19 was a beta version release.

So assuming you are on 25.24 (which is the current non-beta version), your issue is probably caused by the fact that with the 25.24 update the Edge now uses a different way to connect to a computer, which is called MTP.

Unfortunately macOS doesn't support MTP very well. This results in the device not being accessible anymore via Finder (it won't get shown as a volume). And the second issue is that only one application can connect with an MTP device at a time.

Because Garmin Express usually runs in the background, other applications (like Basecamp) cannot access the Edge. So you need to fully quit Express before starting Basecamp.

If you need to access the files on the Edge, you now need a 3rd party utility like OpenMTP to do so.

I've updated today to 25.24. The problems are still the same. Even when I have closed Garmin Express Program, Basecamp does not find my garmin edge1040 solar anymore. As soon as I connect my device with my MacBook Air (M2, 2002, Sonoma  14.6.1) the connection symbol appears as well as an underlined triangle in the lower right hand of the screen (eject symbol). 

Downloading OpenMTP also has not given me access to my garmin device. It is also not recognized by OpenMTP.

Do You know whether I can download an older firmware release to connect my device again with my Mac? My older garmin edge 830 is working still fine with basecamp and my Mac in the current configuration.

I'm very unhappy about the software policy of garmin, since this is not the first time that major problems in the connection with MacComputers occur.