How can I stop my Apple ID from logging me out during data transfer?

Have you run Disk Utility's Disk First Aid on all connected drives?

In Disk Utility>View, select Show all Devices, highlight the top left entry.

Run Disk First Aid on all items in the left panel, from top down.

Are you running any VPN, Anti-Virus, or Cleaning apps?

We need to see what all is running, a report from this will not display any personal info...

Using EtreCheck - Apple Community

EtreCheck is a FREE simple little diagnostic tool to display the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to help people help you with your Mac. It will not display any personal info.

https://www.etrecheck.com/

Thanks for Old Toad’s etrecheck instructions…

Slow iMac 2017 - Apple Community

System Settings>Network, top of window>Locations>Edit Locations, little plus icon, give it a name.

1. On your Mac, choose Apple menu  > System Settings, then click Network  in the sidebar. (You may need to scroll down.)
2. Click the Action pop-up menu  on the right, then choose Set Service Order.
3. Drag services into the order you want.
4. Click OK.

The interface that connects to the Internet should be dragged to the top of the list.

System Settings>Network>choose interface>Advanced>Proxies Tab, make sure none are set, like for HTTP & HTTPS.

System Setttings>Network, click a network service on the right, click Details, then click DNS. (You may need to scroll down.)

Enter these numbers...

8.8.8.8

8.8.4.4

1.1.1.1

9.9.9.9

Apply.

Do they Resume once connected again?

Tell me about your Internet connection please.