Is the Cloudflare proposed ODOH protocol a thing that could improve Bitcoin node privacy?
Bitcoin running with onlynet=onion is severely insecure, nobody should ever be running the software in this mode. There is no sybil protection, it is completely feasible to operate an unlimited number of HS peers and prevent a node from ever connecting to one which will give them a true vision of network consensus. There is no cost to performing this attack whatsoever.

one has to either leave DNS queries enabled (which could potentially reveal a user is running Bitcoin)

DNS queries can be proxied as well.

Does (hypothetically) using the ODOH protocol for the initial node discovery make any sense from the privacy perspective?

I doubt it makes any meaningful difference, especially as seeding is typically only something which happens for initial startup of a node and likely never again. You're almost never going to be able to hide that you're running a Bitcoin node from your ISP, even by using a proxy the traffic patterns are very obviously Bitcoin.