Can you transfer Time Machine 10.14 (Mojave) to Time Machine 10.15 (Catalina)?

Yes, that's exactly the problem I thought I read and what I encountered with respect to going from Mojave to Catalina with respect to TM. I raised this question because my new TM drive, started when I switched to Catalina in the beginning of 2020, stopped working and, as I now will have to use a new drive, wanted to check if I could load it with my pre-Catalina archive of TM. I don't think that I will be able to do that. I wonder if some third party has some software/workaround to allow loading TM files created under Mojave to be on the same drive/in continuity with Catalina?

That's very helpful, but for some reason I feel unsure. That is, when I upgraded from an earlier MAC OS to Catalina, I received advice that the existing TM (Time Machine) files (from the earlier OS) could not be read from Catalina's TM. I wanted to start a new external drive so as to accommodate more space for my TM since my existing external drive was running out of space. I wonder what I had incorrect?