USB Adapter for wireless internet that matches macOS 13.3.1

WiFi not staying connected.

If your router is using WPA2/WPA3 Mixed Mode “Wireless Protected Access”, try changing your router to just WPA2. Not all routers play nice with Macs that are trying to use WPA2. I cannot give you exact instructions, each home router is different. Check with your router manufacture.

If switching to just WPA2 does not improve the situation, then you can always switch back to WPA2/WPA3 Mixed Mode.

Try disabling IPv6:

Monterey: System Preferences -> Network -> Select Interface in left column -> Advanced (button) -> TCP/IP (tab) -> Configure IPv6 -> Link-local only

Ventura: System Settings -> Network -> Wi-Fi -> Details -> TCP/IP (tab) -> Configure IPv6 -> Link-Local Only

All you really need to do is find one with the correct port type or use a simple passthrough adapter. After that it's trial and error to find the one that works best.

The fact that neither the internal network nor an external adapter works speaks to the problem being something else. There is nothing special about the 13.3.1 version's network card, but that doesn't mean it can't have problems.

First thing I'd do is reinstall the OS from the Recovery Panel: Command R at startup. Sounds to me your OS is damaged.