Upgraded to CiviCRM 5.34.0 and extensions broke
Looking at CRM/Extension/Browser.php where that error is generated, I would expect it to show a URL between the at and could in your message.  So Civi isn't calculating the repository URL.
Tracing the code a bit, it seems that the URL should be calculated in CRM_Extension_System::getRepositoryUrl(), which pulls it from the ext_repo_url setting.
Here's what I would try, in order:

Clear the CiviCRM cache, that's probably the issue anyway.
Confirm that &lt;civiroot&gt;/settings/Extension.setting.php defines ext_repo_url with the default value of https://civicrm.org/extdir/ver={ver}|cms={uf}.
Check the civicrm_setting table for a record with a name of ext_repo_url.  If one exists, this is overriding the default; remove it.
Alternatively, add a setting (via API Explorer, or in civicrm.settings.php - see Override settings in the docs) to set ext_repo_url to
https://civicrm.org/extdir/ver={ver}|cms={uf}.  This should force the correct URL to be generated.