It at least checks for updates (one forum post says once a week), but I’d expect that to be quite fast.
mono can likely do memory garbage collection when it likes, but all those mono-sgen look odd to me. Perhaps you could get a process tree, or at least run ps to sample parent PIDs to check their origins.
Other people here are on Linux more, but I’m used to seeing one mono-sgen even on busy Duplicati.
You could try using netstat or lsof to see what has port 8200. Also confirm you can telnet-connect. Duplicati doesn’t log routine web server traffic because it’s constantly polled when things are working. Packet capture such as tcpdump, wireshark, or tshark could find what’s going on, if you’re into that…
Duplicati.Server.exe has --log-file and --log-level options, if you want to make a big file to read. Generally this is redundant with job log, but you’re wondering what may be going on between job runs.