What is your Roon Core server exactly?
If it’s a Nucleus(+) or ROCK machine then no. The data from the external drive connected to the core flows over your network to the control PC and back to the core’s internal disk.
This also doesn’t sound like you’re able to take the network out of the loop.
If it’s a self setup machine running a full-featured supported (for Roon Server) OS like Windows, MacOS or Linux where you can login an perform this action then yes. In this case keep using this direct copy method.
Good if this is your Roon Core.
~5 Mbit/s for ~940 MB in ~30 Min. looks like a great improvement compared to the figures you provided before, but still far away from any decent network throughput. I don’t know the Google Nest WiFi product(s). You can’t copy files faster over the network than your network throughput allows you too. You may have to ask someone you know and who has some networking/WiFi knowledge to have a look at your network or ask (pay) a professional to fix up things for you. Good luck.