Of course your phone has a short runtime, it both has a small battery and it's 3 years old so the battery's worn out. One of the main reasons why small phones remain a niche is that improvements in battery technology have been far outpaced by improvements in SoCs, so the easiest way to improve a device's battery life vs. the older model is to make it larger so it can fit a bigger battery. Even when it was new, the regular iPhone 13 had a 3220 mAh battery while the 13 mini had a 2400 mAh battery, despite both having the same processor. You end up sacrificing battery life to achieve the small size.

I have found low-battery mode to be very useful. I also have background updates turned off for most apps, but this greatly extends my battery life. When traveling, I turn it on by default at the beginning of the day.