I've also been having weird issues with the steam deck downloading for some reason and couldn't figure it out. I use the dock so it's using a wired connection (but the same thing happens on WiFi) and I have gigabit Internet, will get maybe 150mbps for a moment, then drops down to max 15mbps or slower but doesn't outright stop like yours.
If you do a speed test in desktop mode via a browser what speeds do you get? I'm all but positive this is something specific to steams cdns. I also use a pihole but bypassed it for testing and it made no difference. What's your download region set to in the steam settings? I'm on the east coast and tried a couple different nearby locations with no effect.
I did stumble on that issue, but no I have a 1tb SSD installed with tons of free space on it and it's performance seems totally fine - I can transfer a game from my PC to the deck at 500+mbps. I've just kinda given up and been using my pc to download larger stuff first and transferring it as a workaround for now.