How do I troubleshoot slow network connections while switching to Linux?

Start by separating name resolution from the connection itself. When a site is slow to open, compare how long it takes to resolve its hostname with how long it takes to reach an IP address. The commands time getent hosts example.com and ping -c 4 1.1.1.1 are a reasonable starting point.

If the IP responds promptly but hostname lookups are slow, check which DNS servers your connection is using. That would be a different problem from a slow wireless link. A failed ping alone is not conclusive, since some hosts block it.

The extender is acting as a bridge here. Linux generally sees the laptop's Ethernet adapter, not the extender's wireless chipset, so I wouldn't buy another adapter based on the extender chipset alone.

If possible, test a direct Ethernet connection to the router, even temporarily. Then compare that with the extender and the built-in Wi-Fi. That should help narrow down whether the delay is tied to one path or happens across all of them.

Check whether the Wi-Fi adapter is detected and which driver it is using before installing anything else. lspci -nnk can show the device and its kernel driver, and journalctl -k can show firmware or driver errors from the current boot.

Some distributions offer additional proprietary software or firmware during installation, but that is not a universal fix. The exact adapter, distribution, kernel version and any errors matter more than the distribution name alone.

Since the trouble has shown up across several distributions, keep the next test simple and avoid changing a bunch of network settings at once. Note the commands and changes you make so you can undo them.

For a useful follow-up, share the distribution and kernel version, which connection you tested, and whether the delay affects both hostname lookups and direct IP connections. That gives people something concrete to work with instead of guessing at drivers.