In general you don't want governments or just anyone to know you are transacting in Bitcoin and PSBT shows you are in.
PSBT file is relative small, you could always hide it inside regular file (e.g. png or docx).
I just would like a minimalistic setup where the entire process is done with Bitcoin Core and you don't need to install anything else to store encrypted data.
You could use built-in archiving software. But obviously
As far as cloud storage. All of these "anonymous email" services aren't really anonymous. And "anonymous cloud services" require that you dox yourself via paying a subscription usually. You would to find one that accepts BTC and mix the coins and hope it all goes well.
I could use Tor to sign up to a brand new ProtonMail account, and then upload an encrypted PSBT and save it as a draft. When I arrive at my destination, I use Tor to access the ProtonMail account, download and then decrypt the PSBT.
According to
https://protonmail.com/support/knowledge-base/human-verification/, it's harder than you expected. If they decide to ask email or SMS as verification, your only option is either perform the verification or upgrade to paid plan using Bitcoin.