

Any downstream fork of Firefox. All the good of Firefox and Gecko (including addons), none of the Mozilla corporation. The most popular ones seem to be Waterfox and Floorp (for “most users”) and LibreWolf for privacy diehards.
You can copy your Firefox profile folder directly into a fork’s profile folder and have everything exactly as you left it (though doing this to Librewolf will likely overwrite some of Librewolf’s privacy-first default settings like purging history every time the browser closes)
On iOS you are already stuck with every browser being a Safari+Webkit skin. Even Chrome “Isn’t chromium” on iphones. But mobile iOS “Firefox” can still use Mozilla (or self-hosted) sync to desktop Waterfox (etc).
On iOS your option is Safari and that’s what you’ve been using, even if the icon says Firefox or Chrome or Brave. It’s against Apple store TOS to have a web browser with an engine in it - they all have to be skins for Safari (Webkit). Different “iOS Browsers” will offer features on top of the Safari that actually does the browsing though, like account sync or built-in ad filtering.
The only platforms out there that are more hostile to open source software than iOS are like, game consoles.