Like you, I am not the most mechanically-inclined person. Like you, I can fix a flat tire. I recently saw a YouTube video on how to remove the rear wheel, and that was tremendously helpful the last time I had to fix a puncture. I know how to take in the slack on brake cables, clean and oil the chain, and not a lot else.
My lack of skills has not prevented me from bicycle touring. However, I take my bike in for a tuneup before every big trip. On occasion, the mechanic has identified something that needs TLC or replacement, e.g., brake pads nearing the end of their life. So I don't normally have significant mechanical issues on my tours.
There have been times I've needed to find a bicycle shop while on a tour. Sometimes the problem was just beyond my capability to resolve. Other times, the problem was due to unexpected circumstances, like being forced to ride on a freshly paved surface, which destroyed my tires and completely gummed up the drivetrain. In the end, these problems just became part of the overall experience. In the last instance, I had a nice conversation with the mechanic.
The more that you know about bicycle repairs, the better off you will be. If I were riding off into retirement, I would be tempted to take a few hands-on courses on bike maintenance.