Are you using Postman on a company network, on a VPN or behind a firewall? There’s potential that the connections from the app are being blocked on your network.
Using the Web Version is an alternative as you mentioned that still works or if you’re using vscode as your IDE, we have an extension on that platform. Not ideal but these can unblock you to a certain extent.
Could you try getting the logs for the app and sending these to help@postman.com to see if the support team can help you out here and provide a solution for your situation.
The app is working fine for the majority of users so there is something specific happening here that i’m sure we can get sorted for you.