Yep, but with just "Automatically reconnect, if it stalls" increased, I would still get "Host is not communicating for more than 15 seconds" for each large file. Which is sort of annoying.

For my use case, increasing the general "timeout" setting seem to work OK – the connection is reliable enough and does not get actually stuck (at least, I had no problems with that during the last 2 days).

You can instead disable (or prolong) the reconnect on stall:
https://winscp.net/eng/docs/ui_pref_resume

The remote checksum calculation via SSH (as the sync criterion) seem to not work well with huge files – the files that take, say 20 minutes for their checksum to be calculated.

In WinSCP 6.3.6, I get "Host is not communicating for more than 15 seconds" warning shortly after the remote file checksum calculation is started (in ~15 seconds). Next, WinSCP waits for the "Automatic reconnect" timeout (if it's enabled in Preferences -> Transfer -> Endurance) and abandons the connection (BTW, the sha256sum process on the remote server continues to run).

As a workaround, it is possible to simply increase the "timeout" in the server connection settings (e.g. to 5000sec) for the Synchronization to work. But this is still just a workaround.

Technically speaking, sha256sum does not seem to provide any "--progress" or something, thus I'm not sure if there's an easy way to monitor the real progress. Maybe, as a better workaround, it is possible to add something like "expected minimum sha256sum speed (MB/s)" setting in WinSCP and calculate the actual timeout based on the file size.