I presume the old, 3.8.3 MyEclipse would still be usable, in case the new one does not inherit my license key, right?
Yes it will still be usable, you can adjust ‘which one’ is active by navigate to Help > Soft Updates > Manage Configs, and right-clicking and “Disabling” one or the other then restarting.
I am being extremely cautious because I do not have my license key with me. It’s stashed away in some PDF file on a machine at home.
IIRC you can request it from the site using the Member Features… also you can do Help > About > Configuration Details, and look for the key “LICENSE_KEY”, and that should be it if you need it.