Hi Jen, thank you for tackling this, and thank you for your awesome work with Backdrop over the years. I really like the software.
To be honest, I am not a big search expert, I have similar settings for the Search API for each site. I used to rent a dedicated service in Germany (https://hosted-solr.com/), but the experience was not very impressive speed-wise, canceled it a few months ago. I use the Virtual Hosting Server here, it's a quite well-known company in Switzerland, but not a dedicated Drupal provider: https://www.nine.ch/en/home
The plan is to rent Nine's SOLR option (again) and make some tests... because right now I use Database Search for all sites, including sites with automplete like this one (try e.g. "Hamilton" in search field) https://zeitshop.ch/
I would be pretty happy to have the current state of Search API in Backdrop CMS, including the comprehensive settings on a field level, e.g. Regular Expressions on a per-field base. Just one example: this search here showed ALL results with two "1" in there https://binderrehab.ch/de/skusearch?search=01-1001 (hundreds of results). The problem could be solved with RegEx... it's an SMB client, but search becomes quickly "enterprisey" in every project.
Regards from DrupalCamp Spain (and I hope to make it to Minneapolis next spring)