After updating to Edge Beta version 120.0.2210.49 (released on December 1st, 2023), the "Application" tab in the developer tools started working again as expected on all of my devices. In the release notes for this version (https://learn.microsoft.com/en-us/deployedge/microsoft-edge-relnote-beta-channel), it says "Fixed various bugs and performance issues". Presumably the broken "Application" tab in the dev tools was one of them.