Looking for WebKit engine options after Jailbreak

I'm currently on an iPhone 13 mini, running iOS 16.1.2. It looks like I'm just too late to do a delayed OTA to iOS 18, and perhaps I'll be happy I wasn't able to do that now. The trouble I have is that a lot of websites will not load in chrome or safari, because of something called a "WebKit Engine, and I'm wondering if there would be some options for a different WebKit engine if I was to jailbreak this phone.

I don't know a lot about these WebKit engines, or how to talk about them intelligently, I just know that I can't load certain websites at all, for example Claude.AI.

Does anyone know if jailbreak options might provide a different alternative for me, so that I might be able to better use these websites that require updated versions of these WebKit engines?