Far as I can tell, someone wrote:
We've spoken to a marine surveyor we might
hire who says that the engine can be tested to some extent on land but
that we really should put the boat in the water and check it out.

So I guess your surveyor isn't Harry. He's never been out on a boat.

Seems reasonable - but my question is one about procedure. Who usually pays
for the marina to put boat in and take it out again in such a case -
buyer or seller?

If you buy the boat, the seller should absorbe the cost of the survey.
If you don't buy it, you do.