You can use either iPerf3 or OpenSpeedTest to test your LAN speed. Ideally, you will have one of the laptops connected via ethernet to test the wifi speed of the other laptop then reverse and test the other laptop's wifi.
Hmm i would advise to try test with iperf3 too just in case.
i just caught myself not so long ago with some interesting issue with steam and it was making me nuts
it seems when i was downloading, my speeds kept interrupting even got worse to 100mb/s at some point (while i got 1gb/s speed), then it was the ssd, it seemed i used those cheaper drives with QLC cache which is very fast slow.
But that is about writing, in your case it is copying and im not sure if it then also does caching?
I'm not assuming anything, I'm troubleshooting. But yes, that could be the issue. Also, when using iPerf3 I've found adding '-w 4M' to the command gives better results when testing over wireless.