Who needs to store porn anymore when it's all free online. Internet's wonderful isn't it?
The Apps tab is far more efficient at checking for updates than the plugins tab is due to a different design consideration. What your system is probably doing (I couldn't see if you hit the Plugins tab during the period covered by the diagnostics) is that Settings - Notification Settings, check for plugin updates is enabled.
This causes the Plugins tab to check for updates as soon as you go there and if it doesn't complete in a reasonable time (120 seconds) then the spinner actually never disappears.
Disable that setting and it'll probably let you in.
Now, what are these DNS servers you have the system pointed to?
DNS_SERVER1="192.168.172.10"
DNS_SERVER2="192.168.172.11"
A piHole / pfSense server? If these aren't properly up and running when checking for updates then it just won't work properly.
Another alternative is to install the AutoUpdate plugin (Set to update no plugins, but still running on a schedule) and still keep the OS not checking for updates on a schedule.
6.10.0 also includes changes to the plugins tab to still allow it to check for updates automatically on a schedule, but it won't stop the page from loading if things are working properly.