OP may be confusing Edge/Brave/Opera with Firefox here, so I can't really blame them for having had the impression that Firefox and Chrome share the same engine.
And in at least one regard it's entirely true: on iOS, everything uses WebKit.
Nope. It was a fork of WebKit which was a fork of KHTML, the engine powering Konqueror. KHTML was developed by the KDE team.
Edit: It was widely speculated that Apple would use gecko for Safari and a shock when they announced they would use the relatively little known KHTML engine. The decision was based on KHTML having much cleaner code. I haven't looked at the Mozilla code in many years, but it was pretty gnarly back then. Lots of old cruft from the Netscape days. In comparison, KHTML was beautiful.
Ken Kocienda's book "Creative Selection: Inside Apple's Design Process During the Golden Age of Steve Jobs" has more details about the Safari team's evaluation of Mozilla code and KHTML. Ken was engineer #2 on the Safari team.
I went looking into this, and it appears that I was confused. Google was a big contributor to Firefox in the early naughties, which is the period I was thinking of. Chrome didn't come out until a good while later.
And in at least one regard it's entirely true: on iOS, everything uses WebKit.