There's no way a 3rd Mobile OS would be remotely close to iOS or Android.
In fact, there have been already a few attempts over the years, and as you can see, even OP who is looking for this didn't know about them.
Here are some examples:
Sailfish OS is a European alternative to dominating mobile operating systems, and the only mobile OS offering an exclusive licensing model for local implementations.
On the market since 2013, and now already in its 4th generation, Sailfish OS offers a secure platform for trusted mobile solutions. With Sailfish OS you can also run Androidâ„¢ apps with our dedicated App Support solution.
Sailfish OS is managed and developed by Finnish company Jolla Ltd.
With Ubuntu Touch, we offer a truly unique mobile experience - a viable alternative to Android and iOS. We provide a free and open-source GNU/Linux-based mobile operating system. One that can be installed and used today.
KaiOS brings the best of smartphones to affordable devices. Hundreds of models worldwide, starting at just $10.
And more...
Realistically speaking, the best thing you can do today is to get a Google Pixel phone and put GrapheneOS on it. It's basically Android without Google. It runs great and works with pretty much all Android apps out there. And you can also just use the web app for the ones that don't publish their apk.