Did this other site have an equivalent catalogue with existing matching field names?

Yes it did.

Having a quick look at the code, I can see the block cache is not being auto-emptied after import.
Does emptying the block cache manually fix the issue?

Automated response: Import tasks are not consistently emptying the block cache

Any background import task that sets mass-import mode should be emptying any block caches that would be invalidated by the import operation.

A few are, but not all.

Make it a standard feature of the tasks system to empty the block cache if mass-import mode was set, and make it so no task import hooks empty block caches manually any more.

I emptied all the caches and nothing appeared on the frontend. Will try again once I've applied this hotfix.

So they show for edit, but there is no category that shows them on the front-end?
Is this a tree catalogue or not?
Can you dump the contents of your catalogue_entries and catalogue_categories tables and email to me?

Was replying to your early comment asking if I'd cleared the block cache, I had. The entries were in the db but not showing in the catalogue. It was a tree catalogue. Not tried the hotfix yet and the test installs are no longer in action but I will try again as it's a nice way to do batch updates.

I think I found the issue, which is fixed in #4752.