Is it normal to walk around an (American) hotel in pajamas?

As a night clerk at a 2 star hotel in the US, I can say it depends, mainly on if you're comfortable with it. Most people wear non-sleep clothes while not in their rooms. However, there are some people who will walk around in pajamas. On very rare occasions, I've even seen people come to breakfast in their pajamas.

Higher star hotels may be more rigid, and I would say that everybody around you is going to be wearing non-sleeping clothes. However, if you're find sticking out a bit to be comfortable, then I would say go for it. I highly doubt anybody will say anything.

The only realistic answer to this question is that there is no answer. Standards of dress in the US are not standardized, except in certain contexts like prisons, the military, certain types of business, Catholic schools, and fancy restaurants. Circa 1960 was the last time in the US when there was some kind of general consensus on what was proper dress in public. That was the era when, for example, people understood that a middle-class man should tip his hat to a middle-class woman on the street, and a black male civil-rights protester would sit down at a whites-only lunch counter and get arrested -- wearing a suit and tie.

Basically, if you're not sure, don't do it. But if you guess wrong, there is no Taliban that is going to come along and haul you off to be flogged. People who disapprove will probably just ignore you, or ridicule you to their friends later on.

If you spend enough time in the US to get attuned to the culture, you will start to pick up on a gazillion and one subtle cultural expectations about dress. But transgressing against those expectations is not a huge cultural blunder. As a random example of how fragmented and complicated things can be, it might or might not be considered OK for the CEO of a technology company to show up for an important business meeting wearing a hoodie sweatshirt; it depends on the specific subsector of the technology sector.

Short answer: no.

In North America, public spaces require public dress. You would not, for example, wear a swimsuit to the restaurant.

Asia is a bit more relaxed - you can walk around a Japanese resort town in what amounts to a housecoat.

In America you can basically wear whatever you want in any situation.... Especially since you're a paying customer at a hotel, it would be VERY rare for you to get anything but, at worst, weird looks. (As long as you aren't actually exposing your genitals. If you are, indecent exposure probably will land you on a sex offender list for years.)

It's America. Wear whatever you're comfortable in. It's more common for women here to wear pajamas if they're not going anywhere fancy, maybe less so for men but who cares? I've worn pajamas to the supermarket on occasion.

Edit: It's not normal, in my experience, to wear pajamas around at a hotel, but it wouldn't be frowned upon.

The line between sleepwear and very casual day wear is pretty fuzzy; frequent travelers may find it convenient to carry sleepwear that can pass as casual clothing. (For example, while I (female) normally sleep in a T shirt like top, when traveling I sleep in a longer nightshirt that looks very much like a loose comfortable dress.)

For both genders a t shirt and sweatpants would be both comfortable to sleep in and unobjectionable in all but formal hotel areas.

Note, though: I am white. I've heard too many stories about non-whites being hassled and harassed in the past year or so to recommend that people of color do anything that stretches the limits of propriety.