Your system information

• Steam client version: 1711147596
• SteamOS version: 3.5.17
• Opted into Steam client beta?: Yes
• Opted into SteamOS beta?: Yes
• Have you checked for updates in Settings > System?: Yes

Please describe your issue in as much detail as possible:

Demonstrative video: https://youtu.be/uw0H4hLMDh4
It should be possible to download from Steam servers and transmit over the local network at the same time. On top of that, after you stop the download on the host machine, the LAN transfer doesn't continue automatically.
I previously reported this on the Steam Forums: https://steamcommunity.com/groups/SteamClientBeta/discussions/0/3841053719661349317/

Steps for reproducing this issue:

1. Use Game File Transfer over Local Network to download game files
2. Start a Download from the Steam servers on the host

Result

Local Network transfer stops while the host is downloading and doesn't continue after the host stops

Expected

The host should be able to simultaneously receive and distribute data