I'm a fucking dolt that dabbles and picks up the gist of things pretty quick, but I'm not authority on anything, so "grain of salt":

You're already familiar with OCR so my naive approach (assuming consistent fields on the documents where you can nab name, case no., form type, blah blah) would be to populate a simple sqlite db with that data and the full paths to the files. But I can write very basic SQL queries, so for your pops you might then need to cobble together some sort of search form. Something for people that don't learn SELECT filepath FROM casedata WHERE name LIKE "%Luigi%"; because they had to manually repair their Jellyfin DB one time when a plugin made a bunch of erroneous entries >:|

Might be a little heavy handed for your needs but I've found paperless-ngx to be amazing.

What is the server are they on?

If they are just on a windows server, then the indexing service is actually good for fast results on a network share. If it's a windows 10/11 pc, I think you need to enable classic search for it to provide results to clients over the network.

Alternatively I believe everything (the program) supports indexing network locations.

What's a bajillion? If the OCR output is less than a few GB, which is a heck of a lot of text (like a million pages), just grepping the files is not too bad. Maybe a second or two. Otherwise you need search software. solr.apache.org is what I'm used to but there are tons of options.