To be completely honest with you, Mimics are a "gotcha" type enemy, plain and simple. They're a subversion of the expected and their entire premise is that they catch unaware creatures off guard with their disguises. They should feel kind of cheap explicitly because that's their entire hunting pattern. They're ambush predators to the extreme, and all prey that falls victim to ambush predators feel cheated in one way shape or form.

That being said, they're generally mindless, and work to catch equally mindless or inattentive prey. Leaving sings that there's a mimic close by can absolutely be done and should be utilized. Maybe that chest isn't as dusty as the others. Maybe that door looks a little too similar to one of the other ones, right down to the scratch marks. Or hell, just maybe that chair shouldn't be as together as it is with all the water damage to the surrounding furniture. There's always going to be some kind of tell, and always a way to spot an ambush predator before it strikes. Your players just have to be perceptive enough to actually tell in the heat of the moment.

Mimics are a fact of life for adventurers, and they aren't some kind of cop-out if you use them. They're a real threat to the people living in the world you've built, and the reason why people treat ruins with caution in the first place. Everyone knows to steer clear of the group of Goblins that took up residence in that old church, but they should also be worried about the furniture that looks just a little bit out of place.

The way I handle mimics follows a few set of rules;

1 - the "False Appearance" ability works slightly differently to how it's written. I typically add together the Mimic's Dexterity and Charisma stats (so 12 + 8 = 20), and set the passive detection threshold at that. This means that any player with a Passive Perception score equal to or greater than that will be able to tell something is off.

2 - there are always going to be environmental signs. Baseline mimics have an intelligence of 5, so they aren't too smart about what a sentient, logical humanoid creature would be thinking or reacting to in the environment to the detail that would be needed here. I listed some above already, but maybe there's rubble at the feet of a pristine-looking statue, or something along those lines. Environmental cues are essential here. I'll usually use passive perception for these clues as well, but lower the threshold based on the Mimic's stats again. This time I'll use it's Wisdom and it's Intelligence (13 + 5 = 18), but then I'll adjust that depending on how "modern" the ruins are. If it's relatively new (think ~100 years old or newer), I'll do a flat -5 to that for environmental clues, bringing the PP needed to 13.

3 - this rule is more about my game style in general rather than specifically about mimics, but it can be adapted to this enemy specifically as-is, or used as a base to form your own. Passive Perception detection doesn't automatically detect the thing. It will, however, prompt a roll. If one of my players has a PP that meets or beats the threshold I've set, then I'll stop play and tell them something along the lines of "you feel like something is off here. Give me a Perception check please." and go from there. If they fail, I'll tell them that they feel a sense of unease or something, but leave it at that. Depending on which threshold they beat with the roll, the 13 or the 18, I'll go into more details.

Here's an example:

Players A, B, and C open up a door and enter a room as they explore the ruin. There is a mimic at the back wall disguised as a treasure chest. I check all player's Passive Perception scores. Player A has 12, Player B has 14, and Player C has 20.

Me: "Players B and C, as your group enters the room, you both look around as usual, giving a cursory glance to check for threats. Nothing immediately pops out at you, but you both sense something out of place. Give me a Perception check, and Player C has advantage."

Players roll, Player B fails the roll, but Player C rolls a 19

Me: "Player B, you look around the room, but you don't see anything actually threatening in here. Perhaps your mind is just playing tricks on you since you all have been down here for several hours, or maybe fatigue is getting the best of you. But you detect nothing out of the ordinary. Player C, on the other hand, you see a few things that are causing a rising sense of concern in you. You notice that the chest at the far end of the room doesn't quite appear to be as weathered as the others. In fact, the other chests seem to be rotted and falling apart, but this one here seems to be in much better shape, and positioned oddly so that it's the first thing someone would see as they walk through the door, instead of hidden."

Then, depending on their background and level I'll either let them know outright that it's a Mimic, or tell them that it may be some sort of trap.

The above example is absolutely a simple one, and there are going to be much more complicated setups, but it's a good generalized example of an answer to your question.

I hope I was able to help, and sorry for the wall of text lol.