I have found a few references that claim that the Postgres DBD driver (DBD::Pg) can be used for this purpose

Can you give those references?

UPDATE:

I find on the h2 site that the postgres jdbc driver can be used and that there are so-called "compatibility modes". And that one of those compatibility modes is a postgres compatibility mode:

H2 compatibility modes

Just for reference, here is the postgres jdbc driver

P.S.
Funny how they 'qualify' database features: postgresql gets a glaring red "No" for "Pure Java". Fair enough, but it still made me laugh :)

I also think that the "No" for postgres' "Linked tables" is wrong. Do not the myriad FDW drivers amount to the same thing?

The 'In-Memory Mode' and 'Embedded Mode (Java)' seems to be the interesting part of H2.