But can I have one row that holds all the databases?

You may want to use the $$ way to declare strings for your examples. Something like:

-- Create a todo for "frectonz"

UPDATE people

SET database = execute_sqlite(

    database,

    $sqlite$INSERT INTO todos VALUES ('solve multitenancy')$sqlite$

)

WHERE name = 'frectonz';

That’s fun, but I think I'll just use an SQLite foreign data wrapper instead.

I think the right approach would be to store the sqlite database as a varlena type that can be TOASTed and then "expanded" using the Expanded Datum API so that it's a live open database connection for the life of the transaction:

https://www.postgresql.org/docs/17/xtypes.html#XTYPES-TOAST

https://github.com/postgres/postgres/blob/master/src/include...

Ok, hear me out: what if we make something that takes a postgres database dir, tars it together and encodes it as a binary blob in SQLite?

We could have SQLite within postgres within sqlite within postgres! Is it practical or even slightly useful? Of course not - but it's SQL databases all the way down. Not that this is a good thing in itself.