Years ago I built a 24X28 freestanding garage. My wife wanted two separate doors, I wanted a single 16' wide. It is a pain to park two cars side by side using the 16' door. Why are they always right, lol...
Just an opinion, your situation may be very different...
a standard two car garage door is 16 x 7. Going wider is doable, just remember that all the materials for the engineering on these garage doors are based around 16', going wider means more weight, more stress on the hardware and materials. Tread lightly, use trusted and old companies for the manufacture.
Using an engineered beam or steel is the only way too go across the head. It's super easy, and reasonable, for an structural engineer to do, which then makes the permitting and installing (spec) a piece of cake.
I would open the wall to check to see if that section is load bearing. It may not be, as most garages are built with the beam extending all the way across both openings. That way if a car jumps into gear or some kind of accident happens where someone drives into that small section, the entire house wouldn't come down.
That stem wall above is bearing right through that center column. I would talk to my PE about two ways of picking up the loads-
First would be doing an I beam straight across the opening and picking up the loads on 2 heavy wall columns on the right and left corners.
The other way would be to possibly do a steel flush "T" beam arrangement running back through the garage after picking up the front load. This way you could share the load across the area without loosing headroom.
Of coarse this is total speculation without being there and doing an exploratory on it. I do high end residential work in a very niche market and get challenged by this type of scenario alot. There is a couple of options for you, but get a good structural guy there to do the calcs for you, cause there is definitely some weight there. And I don't know your local codes, but I would say it would surely need permitting!