How do I get logs from my dropbear-initramfs SSH host?
After running through several rabbit holes, I finally found this post describing how newer SSH clients are starting to disable ssh-rsa authentication. Turns out that the solution was to temporarily add PubkeyAcceptedKeyTypes +ssh-rsa to my SSH config for this server. The long-term solution is to update dropbear, but this works for now.
The strange root-XXXXX folder is as it should be apparently.