is it "more correct" to use Search Applications here rather than App Search for this type of solution?
you just want to open all the cans of worms, don't you?
App Search, like Workplace Search, is a product that is hosted in the Enterprise Search Server. These products came from an acquisition of Swiftype back in the day. They're both good products, but they were built as consumers of Elastic products, not as native products. So there's always been this tension where power users struggle to leverage the Elasticsearch primatives when they're using Enterprise Search products.
The migration path away from Workplace Search is clear, and while it doesn't have a concrete deprecation timeline yet, it's pretty obvious that it's coming.
App Search has historically been much more popular, and therefore is going to take a lot more from us to provide a migration path to all native Elasticsearch stack primitives. Search Applications (we're running out of names, aren't we?) are a first step towards eventually offering all of App Search's great features as an Elasticsearch-centric product. Some things (synonyms, curations, analytic dashboards, meta-search) have been replicated. Other things (UI generating easy-button, modern relevance OOTB, opinionated mapping defaults) have not been.
Search Applications are definitely a valid product for you to investigate. They'll probably set you up for longer-term (decades vs years) success. But you also might have to do some heavier lifting. And choosing App Search now won't be as problematic as choosing Workplace Search now, because it's large popularity will ensure a really smooth migration path if/when it does come to an end-of-life (for which there is none on any horizon I'm aware of).
If you look into Search Applications, instead of Search UI, you'll want to look at the Search Application Client, which is the react libarary analog for bootstrapping a modern search experience.
Since I've decided we're now friends, I'll share a link to this (admittedly still rough, very much just an example) example app that uses Flask+Search Application Client (react) to show off how to search multiple connectors, similar to how Workplace Search provides a UI for multiple content sources. I'll eventually write a blog that goes along with this app. Stay tuned to the Elastic Search Labs Blog.
DO NOT just copy this code. This is for inspiration only, and comes without warranty. But I figure it might help you bridge the gap between the Search Application Client docs and reproducing the Workplace Search UI.