Next step might be to confirm the power supply. I have 3 Pi’s and had issues with one that was related to a cheap wall wart.
At least it’s not an OpenWrt or config issue. 
Nevermind, it seems that packet loss issue was unrelated and was because of the piece of trash network switch (the same one in that thread I linked to concerning EEE) that I moved closer to my desktop... TIme to get rid of it for good. Sorry about that.
Just to be sure, I ran iperf3 from Alpine through the "good" switch closer to the Pi 4, and that works perfectly fine in both directions; full gigabit with no packet loss.
Anyways, I did still try a different power supply like you suggested. It's been using a USB-C phone charger that's about 5 years old, so I tried a newer one that outputs a slightly higher voltage (5.05V as opposed to 4.9V, according to the USB-C tester I used), but the DNS problem persisted. They're both rated for 5V 3A, just to be clear.
I finally got the time to test this with Alpine instead of OpenWrt on the Pi, with a minimal setup on the Alpine Pi running dnsmasq (the Pi is manually specified as the DNS server, while internet access goes through my ISP-provided gateway). Somehow, pip install works fine there; the Pi receives the same exact DNS query from my Alpine M720q without the packets getting corrupted. nslookup works fine as well. I then put back the SD card for OpenWrt, and the problem's back again. I guess that rules out hardware issues??