I have rarely mistapped, but it hasn't really been enough to be an issue (with me, it's usually mistargeting a wand by a square). I don't think I've ever had a zoom turn into a tap. That might be just the touchscreen in question.
So, couple things you can maybe do.
You could use a device less-prone to it. I assume that you don't want to get a new device just to play SPD (though I can imagine that if you get mistaps in SPD, there might be other apps where it's also frustrating).
You can try cleaning the device screen. Probably won't help, but won't hurt much either. It'd be the first thing I'd try.
You can tap to interrupt movement. That's not gonna help if even one step is enough to do you in, though.
You can use a USB or Bluetooth pointing device, like a mouse or trackball, if you are willing to carry them.
You can use an attached USB touchscreen, if you are willing to carry one. That will have different touch detection hardware and can be larger, easier to avoid mistaps in gaps.
You can use a USB or Bluetooth keyboard, if you're willing to carry one. There are some small, folding keyboards the size of a smartphone, and they provide some perks, like the ability to do reasonable text entry. That has a physical key for search, and quickslot hotkeys. I don't know whether there is (currently) a keyboard binding for zooming and panning other than default zoom, going off the wiki keybindings page:
https://pixeldungeon.fandom.com/wiki/User_interface
If you also have a laptop and are willing to carry one, you can play there (and it has some nice perks, like physical keys). SPD is not a terribly resource-intensive game, and a used laptop can be had on eBay fairly inexpensively -- it doesn't need latest-and-greatest hardware.
It might be possible for developers to change the SPD interface to deal better with touchscreens that are a little twitchy (maybe have an alternate zoom method?), but I don't know if there's going to be a fantastic solution...confirming each move is gonna be agonizing. Right now, the only option is to adjust interface scale (which might help with mistaps hitting the gap). You can also reposition the toolbar -- I don't know if that helps with mistaps in the gap for you at all.
EDIT: Touchscreens work via capacitance, so how moist your fingers are is a factor. My phone has impressed me with how well it works even when my fingers are outright wet (though not as well as if I dry them), like with condensation from a drink, but according to this, for people with dry hands, this can be an issue:
https://www.macintoshhowto.com/iphone/ipod-or-iphone-difficulties-with-dry-fingers.html?amp=1
Some people have difficulty controlling the touchscreen on an iPad or iPhone with their fingers, especially older people. The iPhone touch sensitive screen works on capacitance and it does not respond well to dry fingers.
Older people tend to have dryer fingers. Often they have to press the touchscreen on the iPhone very hard and I have met one or two people where their iPhone or iPad will not respond to their fingers at all. Thankfully there is a very simple solution. Simply Moisturise your hands with a water-based moisturiser! I find “MooGoo” to be particularly good.
I've never done that, but I suppose it might be worth a shot -- or, if you're in a very damp environment, getting condensation on the screen or something, could try wiping the screen or fingers dry with a shirt.