Hi @loparev, we're running into the same issue.
We've setup a new Drupal environment to isolate the issue: Drupal: 11.2.2 Tmgmt: 8.x-1.17 Tmgmt Smartling: 8.x-9.17
We've used the context debug submodule which works as advertised. The issue however only occurs when trying to upload unpublished pages, in combination with the queue worker running from command line.
It looks like the code, copied from masquerade, on its own (handled with curl afterwards) doesn't handle sessions completely. Masquerade does a redirect on which the Symfony frameworks handles the session correctly and sets the cookie in a response listener.
To dive deeper into the issue, dumping the cookies from modules/contrib/tmgmt_smartling/src/Context/ContextUserAuth.php's getCookies()
looks like SSESSc2b280e207aa821b24606f896b740d6d=
. As you can see it lacks the session_id value.
It's probably because the queue is handled via command line (cron)? Let me know if you need more information to reproduce on your end.