I own Cubase 10 Pro, and unfortunately I lost my USB-eLicenser dongle.
I have already contacted Steinberg Support on August 4 and received a confirmation that my support request was received, but I have not received any reply yet.
Is there any way to recover my license or move it to the new Steinberg licensing system?
Recovering your Cubase Pro 10 license, so that you can use it again, is not possible, but you can still update it to the latest Cubase Pro 15. The important point is that your old license is registered in your Steinberg online profile.
What I said is there’s only two ways the eLicenser can remember which licenses you have. Either they are stored in a physical USB eLicenser or a soft eLicenser which must be synced to your Steinberg account manually. In OPs case, he lost the USB eLicenser, so unless those licenses are synced to his Steinberg account (which you can do from the eLicenser software even for dongle licenses), there’s no way to get those back. (There might be, but it most likely involves some long process of sending Steinberg invoices proving you own the software you need licenses for)
There’s no way to “convert” a Cubase 10-11 license to the new activation model. Well, you can upgrade to Cubase 15.