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.
If only one could open the back and replace the battery, the thing that has been known to everybody to wear out while the rest of the device is perfectly functional. One could only dream of such advanced technology. Maybe in 10 years.
You can. Or at least Apple can (for which they’ll charge you $80 or so). Sure, you can’t “hot swap” during the day, but if you like the size, it seems well worth the expense to get a new battery installed.
I know you're trying to make a point or something, but Apple or an independent service center will do just that for not much more than the price of the battery.
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.
I have an automation that turns it on whenever I take the phone off the charger. You can also set it up with locations. So I have an automation that tweaks a few settings when I get to one of the disney parks here in FL. It's usually keep the screen fairly dim on manual brightness, but set it to auto there. Its really hard to see the screen when it's bright in the great big room.