Can't that just be done by sealing to PCRs? By protecting the unsealing key with PCR which depends on the OS (I usually use the secure boot signing key PCRs since they are different between systems and stable across updates) and some PCR which gets extended by the OS (or for stuff stored in NV making it readlocked during boot). Then any process that launches later can no longer access it and booting another OS also doesn't help.
That helps with FDE (except to the extent that one might want to connect an encrypted device after boot), but it doesn't help in the slightest with SSH keys. The TPM has nothing remotely resembling per-user PCRs.