As Nigel mentioned, the errors should be resolved.
Turning off debug logging is no solution for that, they need to be addressed in the related Support or Developers of those plugins if not related to Toolset.
If this cannot be done, we should disable those plugins now to test further with Toolset on your site.
Can we do that on the site you submitted us access to?
The best would be if we could enable only Toolset there, and Theme twenty nineteen.
If this isn't possible, there is not much else to do but creating a duplicate one way or another.
We can use tools like WP All In one, Duplicator PRO or you can send us a dump of the database and a copy of the WordPress install, too, this can help to recreate it locally and finding the issue.
Note also you use a plugin called Post Types Order, known to have caused massive issues in past on Types relationships, this could still be an issue.
Wordfence Security is another one I'd suggest to try disabling as if overtuned it can break several backend AJAX calls (used when connecting posts)
We need to at least test this with no other plugins and a native Theme before we could proceed more granularly
The problem is clearly due to a hidden fatal Error breaking Admin ajax (that's why the AJAX error).
That error likely comes from either theme or other plugins, so disabling them will show.
Actually, the precise error is "Your security credentials have expired. Please reload the page to get new ones.", which is not the case, I am logged in, so there is a code or plugin telling WordPress I am not logged in, and that makes the error happen.
Can we do that on the very site?
If not we really need a staging duplicate of it, somewhere either online or local to make the first row of such tests.
This is necessary even just because of the long row of non-Toolset errors in the debug log (of today), but as said also to completely solve this problem
I suggest as first an online staging site (this will be for your benefit later as well) or working directly on the live site (maybe put it in staging mode) - a backup would be crucial in this case.
I've enabled all sorts of private reply in case you need to submit me new data - otherwise please can you proceed wit disabling plugins and themes directly on the site?