I wonder if it would’ve been possible for them to use Firefox’s Gecko engine instead, but I don’t know how feasible that idea is.

Considering that Firefox is actually FOSS unlike Chromium, there's absolutely no reason they couldn't have done this. They likely made this choice because it was the easiest, as everyone else is already using Chromium so there's plenty of existing reference material.

If you want a search engine that you can actually control and maintain privacy, while also still having access to DDG, Google, and Bing search results, check out SearXNG.

I host my own instance on a $5/month Linode, so in effect I'm paying $5/month to have completely private search without any influence from corporate overlords.