I'm Archa, one of the cofounders of Insight Browser (https://insightbrowser.com/). We let you deeply customize your search and browsing experience on iOS. You can create extensions on the phone itself, using simple if-then conditions and often without writing any code. For more advanced extensions, you can use JS.
14 years after iOS Safari brought the mobile browser to near-parity with desktop, most mobile browsers are still one-size-fits-all, but the internet isn't one-size-fits-all. It's very long tailed, both in content and in how differently people use it. There is now a generation of users growing up with iOS who still crave the power that's available on desktop. Some mobile browsers come bundled with ad-blocking, and there is a limited way to do extensions in Safari, but extensibility on mobile has been nowhere near desktop. Apple has restricted what developers can do with WKWebView, so we started to look into whether there's ways to work with that but preserve most of the usefulness of extensions.
Some of my personal favorite extensions on Insight right now are — Detect fake Amazon reviews (using Fakemeta) and set price alerts (using CamelCamelCamel); Open a page with cookies disabled or a JS-free version of the page (https://share.insightbrowser.com/11); Make reading articles easier by injecting eye-guiding color gradient on the text (powered by Beeline Reader).
Extensions are automatically suggested as you browse pages, simplifying discovery. We do not log identifiable user data, and if you want to be extra safe about privacy, you can disable all communication with our servers in the settings.
Insight is still very early. On iOS, it's built on top of Firefox. We're excited about open sourcing the iOS Insight codebase once it's better documented, as well as making Insight available on Android and desktop soon. (Btw, if any of this is interesting to you, we're hiring: https://jobs.ashbyhq.com/insight-browser)
A couple of caveats — we don't currently support Apply Pay through Insight. Apple does not allow a regular WKWebView to use Apple Pay, just Safari and SFSafariViewController (https://developer.apple.com/documentation/apple_pay_on_the_w...). We also cannot support syncing bookmarks from other iOS browsers directly, because apps can not access each other's data in any way on iOS. We are however working on a way to import bookmarks from your desktop browsers, and hoping to push that soon!
We'd love to hear what you think of Insight. You can download it on iOS at https://insightbrowser.com/. Please tell us your feedback and ideas. We'd love to help you customize the web as you see fit!