This is actually coming from Joomla's own updates, not the extension updates. It says –in a very idiotic and impossible to troubleshoot by a regular user way– that the TUF (secure update) keys have gotten out of sync. As a result, Joomla can no longer find updates about itself.
Luckily, I had predicted this would and written a workaround. I've included it in Admin Tools which you, conveniently, have installed on your site.
Go to Admin Tools' control panel on your site and click on Reset Joomla! Update. Confirm the action by clicking the big, red button on the new page. Now go to System, Update, Extensions and click on Check For Updates. The message should've gone away now.
If you still get an error, ask your host if they possibly caching the requests your site makes to external sites. Remind them that they should NOT be doing that for Joomla updates, at least not for longer than 1 hour tops.
Nicholas K. Dionysopoulos
Lead Developer and Director
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