I have added this issue to the tracker:
Issue 2334 – Failure when opening two SSH sessions at the same time

Thanks for your report.

Can you send me an email, so I can send you back a debug version of WinSCP to track the problem? Please include a link back to this topic in your email. Also note in this topic that you have sent the email. Thanks.

SFTP-3, WinSCP 5.17.7, problem exists since 5.17.0
Downgrading to 5.15.9 fixes the problem completely.
Background transfer by default on with maximal transfer at a time at 9.

Open multiple files in WinSCP (I used 7) in VS Code to edit. Make an edit to each file then save all. WinSCP attempts to reupload files to host at least ONE of these errors pops up for each file reupload.

Errors:

Server's host key is invalid
Signature from server's host key is invalid
Remote side unexpectedly closed network connection

Sometimes I even get host key fingerprint mismatch when clearly nothing has changed

Mashing OK on all those prompts makes the transfers go through correctly but it's annoying.