> Or even download the full dataset to the client on page load and do the search locally in JavaScript.

That's exactly what I did for a recent hobby project of mine[0]. In my case, I've a db of 30K entries with gzipped size of ~600kb. This serves well for the few hundred visitors I get every day.

[0] https://theshowgrid.com/

Using like operators isn’t full text search. It won’t find results where the words you typed are switched around for example. It wont even work if you accidentally put double spaces. This could work for a toy project but for any respectable app, using like as the search operator will suck. Not to mention it’s unscalable.