Hello LacticWhale, welcome to the Microsoft community, I'll be happy to help you today;
I understand that the network icon shows as Not connected but the internet is working fine;
What exactly is your PC model and manufacturer?
If it's a desktop, what exactly is the model and manufacturer of your motherboard?
Before answering the question I suggest that you run the network adapter troubleshooter;
Press Windows key + i and go to Update & Security;
Click Troubleshooting and then Additional Troubleshooting;
Select Network adapter and click Run the troubleshooter;
Make sure Windows is up to date;
Press Windows key + i and go to Update and Security;
Click Check for updates and do ALL pending updates;
Do a disk cleanup;
Press Windows key + R and type: cleanmgr press Enter;
Click on clean system files and wait for the files to load;
Select all files and click ok to delete them;
Restart the PC and check if the behavior persists;
See you soon!