Is this really the main thing ElasticSearch is used for now? In 2016, I perhaps naively chose ElasticSearch (via AWS's managed service) for an actual user-facing search feature. That service is still running, and now I'm looking to move it to self-hosted, but didn't want to actually run ElasticSearch (or more likely now, OpenSearch). So I looked at the ZincSearch home page, and the quoted heading seems odd.
As for hardware cost needed to run Elasticsearch/Opensearch, it scales down as well as it scales up these days. I have a couple of ~70$/month clusters with millions of documents in each. Not a problem that I need to fix. I can scale them up to cost a lot more and handle billions of documents easily. That's in Elastic Cloud, which would be the expensive option. If you go bare metal, you can get way more bang for your buck obviously. A couple of Xeon machines with some decent amount of CPU/Memory/SSD go a long way.
As for complexity, they make it pretty easy to get started. What you do beyond that is kind of a luxury problem. You get all of these features out of the box but that doesn't mean you have to use them. But it's nice to have the option when you do need them as opposed to running into a brick wall because you are missing key features in these so-called drop in replacements. Depends on your needs. If you don't know the first thing about your search needs, keep it simple and go with mainstream solutions. Sign up with some managed opensearch/elasticsearch provider, get your cluster ready in a few minutes and start throwing some data at it. It's that simple. You can get it running in docker as well if you need something to develop against.
It seems a bit of a rite of passage to be implementing your own search engine these days without being hindered too much by not being completely up to speed with the field of information retrieval and all the wonderful algorithms and sollutions. Guilty of that myself actually; I built a tf/idf implementation at some point. It's not that hard. From there to something that gets close to Elasticsearch/Opensearch/Solr/etc. takes a lot of work and skills, however. There are a few nice solutions out there but also lots that aren't so hot.
I've not used Zincsearch so I'll reserve my judgement. However, their main pitch seems to be that they are cheaper than a thing that is free and partially compatible with it (for ingesting data only) but a bit lightweight (not so scalable, way less features). So maybe pay the difference of 0$ and get something without the limitations that come with being "lightweight"? Just saying. Not a great pitch if you have to name your main competitor in it. Kind of emphasizes that you are trying to catch up rather than disrupt. Does it have any actual things it does better? That should normally be the center piece of a pitch.
Kibana was killer, though.
I personally wouldn't recommend self-hosti gElasticSearch for logs; it's such a commodity now that it cheaper to get something like Datadog or another manage service (but do check the pricing,the last time I checked the managed logging service from Azure was very expensive for what it did).