As pointed out, we're running an ancient system in PC terms, 20 years since IBM dropped all support, 30 years since most active development was stopped, 35 years since OS/2 2.x was basically designed.
We have a mickey mouse tool chain, Paul has done an excellent job of keeping our GCC fork up to date, but it is a fork and parts of it are ancient. Aout object format as an example with no one having the skills and interest in updating to a more modern object format such as ELF or even what Windows currently uses.
We're also missing other tools to lint our code to find obvious bugs like perhaps a missing free(), and those tools probably would require more then 4GB's of ram, especially to check the Qtwebengine.
Browsers are supported by large organizations, Google, Mozilla and Apple are about it. Even MS switched to being based on Google's work. Development happens fast and just keeping up would take a team of people. We saw with Mozilla, one person trying to keep up leads to burn out.
Our platform is missing modern features. Getting IPC working has proved to be hard, we have to run the browsers in --single-process mode, which is unsupported and may be the source of memory leaks. Seems the problem is our TCPIP stack just craps out on local socket operations that are too big.
For a developer to do much, they would have to be a guru, an OS/2 guru, of which there is a severe shortage of. And they would have to be full time, perhaps with a team. Expensive.
I hate to say it, but a modern browser is not likely. A semi-modern one might be possible. Pale Moon could perhaps be done by a decent OS/2 programmer as an example. All the code is in the Mozilla tree and it is a fork, though lots of changes there. Even then a lot of web sites would not work.
We're an ancient platform. I'm lucky as most of what I do, our SeaMonkey is good enough with work arounds like my Credit Union where clicking an icon doesn't work but using the menu does.