I just dealt with this last month, and did exactly what was suggested above. I trimmed away the old gasket material, filled all the gaps up with Lexel sealant, then I stuck on a quarter round PVC trim with more Lexel on both flat faces and shot it in with a few finish nails to keep it in place while the sealant cured.
It all but disappeared once it was painted the same color as the rest of the frame and sidelites. I don’t think I’ll ever be able to replace it in the future with the amount of sealant used, but realistically I’m just trying to get another 10 years out of an existing door unit.
One other note - using mag wheel cleaner and steel wool you can really get the aluminum threshold looking great again. It’ll take off the oxidation and clean up all the years of gunk. I spent about two hours cleaning the threshold before I painted and I’m very glad I did, it made a big difference.