There are lots of definitions.

The atmosphere drops off exponentially with height. That's math for "it gets small really quick as you go higher". You can go to the top of a mountain and notice the change. The change being that pressure is lower, and the density is lower.

You are more likely to notice a lower pressure. Fun story: I drove up pikes peak in Colorado, which goes from around 5000 feet elevation up to 14,000 feet elevation. I had a bag of potato chips (salt and vinegar) in the car. As we were going up, the bag expanded, and you could see it. It looked like it was about to burst. That is because the atmosphere pressure was lower, but the pressure in the bag (it is sealed) stayed the same. By the time we reached the top, it actually popped.

So, where does the atmosphere stop?

Hard to say, because it just gets smaller and smaller (i.e. less dense and less dense). So some people pick 80 km altitude as one point, because the air is so thin you can mostly ignore it.

At 100 km, molecules tend to not collide into each other much at all, so that is another good altitude to call the top.

At 10,000km (the exosphere) the molecules there are 50/50 chance of just escaping earth altogether.

So those are the definitions of boundaries, take your pick.

Does it vary with topography? No. It can vary with subtle changes in gravitational forces, but the dynamics of the atmosphere are a much larger effect.

Vary with tides? Yes, but surprise, not so much the moon, but the sun. The sun heats the atmosphere, every day in a nice 24 hour cycle. That makes tides in the atmosphere, where the heating is a strong effect that the gravitational pull. So that is different than with water, where gravitational pull is the main effect. The sun can cause 24 hour tides, but also 12 hour tides, and some 8 hour tides.