What is "break in" and what difference does it make? In amps? Preamps? Speakers? More?

Right. Evidence suggests the universe itself is like this right down to the smallest details. Even when we say be objective, the root word object is a thing. But then we look closer, there are no things*. There are only processes. We think the things are matter. Solid. Objects. But the supposedly solid objects are all made of electrons whizzing around. Then it turns out not even the electrons are things, they are not objects, that is just how we think of them. Quantum physics however proves the electron is not a thing in one place moving around it is instead a cloud of probabilities. The objective literally is subjective. And, since the cloud nevertheless makes the object, vice versa.

* The actual quote is There are no such things as things. https://www.youtube.com/watch?v=IGhDkh972Zg

As if the blind don't have enough problems without you pestering them to listen to your alleged cables.

Is there a difference in what one hears when it comes to speaker break-in vs. component break-in?

Not really. All start out with whatever fundamental character they have, but thin and etched or grainy, and then over time fill in and round out becoming more palpably real. To whatever extent they are capable of doing this. The differences are only in the details. The over-arching fact of improving with use is the same regardless of whether we are talking about a speaker or cable or component, or even a part like a fuse, cap, diode, or transformer. They are all the same.

Are there levels (quality) where break-in makes no difference?

No.

There are levels where some are run in before shipping. But no one is going to run anything 24/7 for 30 days- and even if they did it would still go through a mini break-in when first hooked up after being banged around in a cold shipping container for who knows how long. Just like every night the gear you had turned off during the day takes a while to warm up and sound its best, so everything brand new goes through the same process, only more so.

Hard to believe after all these years there are still people questioning this. I’m not talking about the OP, who we can excuse for being new. I’m talking about these others still pretending what is staring them right in the face is not really there. What is wrong with audiophiles???