I also like liquid soups with various innards dumped in.
I make mashed potatoes boiled and mashed with masher–completely traditional–and they are neither soft and formless, nor lumpy.
I rarely use power tools–except a mixer for pancakes (and even then I sometimes just shake up the mixture by hand). I rarely strain. When I do, it’s with an All Clad strainer tool.
What is your pancake recipe that uses a mixer? I have a basic cup of AP flour, scant teaspoon of baking powder, hearty pinch of salt, splash of vanilla, tablespoon of sugar (I like turbinado), and just enough milk that the cake will spread to plate size, a bit over an eighth of an inch thick. I use a whisk or a fork, whisking just enough that the batter is thoroughly incorporating the flour fully. Now I want pancakes!
I make the same salsa, but I puree some onion and garlic in there with some sweeter peppers that I’d grilled. Three jalapenos for the kick. Or, I love habaneros, or chiltecpin, which you have growing in your yard (envious.) To find those, I have to go back to Milwaukee. Long drive for little bullet peppers.
Very popular place on the other side of the state from me makes the Swedish cakes on the flattop. Just a huge square they cut up into little ones, and serve with lingenberries. Al Johnson’s is the name. They have goats on the roof.
Pizza or pasta sauce: immersion blender (in the can of Italian tomatoes) for convenience. If I was making a large seasonal batch using fresh tomatoes, I would use a food mill or strainer attachment on the Kitchenaid mixer to remove the seeds because I find the seeds add a subtle hint of bitterness that doesn’t bother me much but if I’m taking the time to make from a large box of tomatoes it’s worth the extra step.
Mayonnaise: immersion blender
Custard style pie like (Hawaiian purple) sweet potato, pumpkin, pecan, key lime: Vitamix
Fesenjun: food processor, if I want the walnuts to be just ever so slightly toothsome. Otherwise, Vitamix for smooth version.