Don’t be hard on yourself, it’s not your fault. Road bike gearing ratios are designed for pros or super fit amateurs. No matter how hard cycling industry tries to tell us that anybody can spin the legs like Froome with something like a 34-32. It is not true. A lot of people, specially those who are new to the sport, would find very hard to climb gradients over 12% with a 34-32 without stopping at some point, let alone spinning.
As others have told you, check your gearing. If the smallest chainring is anything higher than a 34, and/or the bigger rear cog is anything smaller than a 32, you have the wrong gearing for Taiwan climbs (unless you have pro cycling level).
Ideally, you want something even smaller than 50-34 in the front. The problem is that, in most cases, that requires changing your cranks (expensive) and some frames won’t even allow installing something like a 46-30 because they are designed for 53-39.
In the back, 34 or 36 is the biggest than Shimano and SRAM rear derailleurs officially support (not all models). With the newer Shimano rear derailleurs, there are people using 11-40T MTB cassettes without further mods, but Shimano does not recommend it. Although they are pretty conservative with their recommendations.
I think with electronic gears you can mix and match MTB and road components (with Sram for sure). So, some people use MTB rear derailleurs and cassettes with road shifters if they require those gearings. With mechanical shifting, you cannot do that (at least not with Shimano).
Smaller cranks can also help you to increase your cadence (the rpm of your legs). Again, bike brands usually offer a very limited selection of sizes because of economic reasons. This is something that you can check too. Specially if you ever change your cranks.
Oval chainrings can also help, although I am not so sure about this.
In the end, you should try to keep 70 rpm, at least, while climbing. I usually am around 80 while climbing. 90 or more is hard for me to maintain on climbs, even if I have the gears to do so. I am riding 46-30 front and 11-34 back. Of course, no matter what, when you are climbing gradients of 20% or more, you just do what you can.