Plenty of places around the world are still doing COVID tests and plenty of people around the world are still wearing masks. Hell, plenty of people around the world were wearing masks before COVID too, both for protection from other non-COVID viruses, and also just as a basic courtesy to the people around them.
Something Americans don't seem to realize is that the rest of the world has not all had their COVID waves at the same time. Some countries had it worse, others had it better, others started better and got worse, others started worse and got better. Most are still suffering to some degree. Even inside the US it hit different states differently. That's the shitty thing about a new virus - especially one that we utterly failed to eradicate. It doesn't just all come at once and then disappear overnight, it's gonna keep hitting different communities over and over for years, although hopefully less damaging each time.
On topic. The mask thing depends a lot about what kind of mask you choose to wear.
When i headed out on my journey last year, COVID was still causing a lot of trouble in Canada and the US, but also there were really bad forest fires that filled the skies with so much smog it was difficult to breathe. I packed with me a bunch of 3M N95 respirators that came in a tube. I removed them from the tube and put them into a ziplock and tried to keep them at the top of my bag. That style doesn't fold flat, and you don't want to bust the shape otherwise you might not get the tight closure that you're looking for to get full 95% filtering. I ended up giving away a whole bunch because they were too bulky to carry around. That said, you can re-wear N95s a lot, as long as you are getting a good seal, so i survived with just 3-4 of them for a month or two. Try not to drop a beer on one, though, that'll fuck it right proper.
I also carried with me a stack of three-layer disposable surgical masks, which don't provide the same level of protection as N95 respirators, but they still make it a bit easier to deal with smoke and smog, and they also do a decent job blocking so-called droplets, which is like what sprays out when you sneeze, stuff that is heavy enough to fall to the ground. COVID and a few other viruses are not just transmitted through droplets - they can also live for a while in tiny amounts of moisture that float around in the air - so a surgical mask isn't going to protect you from everything... But it should still reduce your exposure to some extent, and (imo more importantly) if you wear it properly then it kinda pushes your breath backwards instead of forwards, so you don't exhale your droplet-laden germs all over other people when you are breathing or talking. How many times you been accidentally hit by someone's spittle when they talk? To me it's just a matter of politeness nowadays to try keep the mask on when i am interacting with another person in an enclosed space. Another bonus is if you keep your mask on most of the day, you avoid absent-mindedly touching your nose and mouth with your hands, which is another source of virus and bacterial transmission. For that benefit you could probably even have one of those hand-sewn cotton ones, although those seem a bit grody to me unless you plan to wash them as often as your underwear.
Obviously this is completely anecdotal, but i traveled for 6 months in and out of crowded areas in Colombia and Panama where i - and most other people - were wearing surgical masks in public, and didn't catch COVID or any other colds/flus/whatevers. The few bucks i spent on surgical masks was money well spent in my books. Way cheaper than visiting a doctor overseas or buying tablets after i got sick, and that'd be true even if there wasn't any COVID. Life is much better when you don't have a random respiratory disease popping into your lungs a couple times every year.
Of course i did get sick once or twice from eating bad shit, but that's a separate problem with an easy solution - don't drink unfiltered water and don't eat shady meat or fish.
So, my recommendation is unless you are going to be in an extremely smoggy area, or spending a lot of time in tight, enclosed spaces with lots of other people who refuse to wear masks, i wouldn't bother with N95 respirators, just get surgical masks. They're super easy to transport, you can buy them anywhere, they're cheap, and they're effortless to put on and take off. Also they work pretty well with glasses. There are some other ones, the so-called KN94 ones that fold flat but when you fold them out they look like a beak... Supposedly they do a better job than surgical masks, but personally i never found them comfortable, my glasses kept slipping off, and i didn't feel like the increased cost was worth it for me. Imo if you want solid protection for certain situations just get a proper N95 respirator or two, and hell with the extra space it takes up in your bag. But you gotta assess your own risk and decide if it's right for you. Maybe folding flat KN94 is worth it for you.
The other thing you might consider is a face shield of some kind. The big plastic ones you sometimes see on airplanes and public transport should be pretty easy to buy or even make if you're handy. Check out the stores in Chinatown. But i had one of those in Panama (mandatory on public transport) and it got busted up real quick. Imo just having a pair of glasses is an acceptable solution. Sure, they're not perfect, but none of this stuff is perfect, it's just about reducing risk. It's not rocket science. More stuff between you and the infection vector is better. Same idea as as a mosquito net or wearing long sleeves. Given that, glasses are easy to find anywhere, you don't look "weird" if you're wearing them, and they at least are gonna block any spray coming straight at your face. If you want to be real careful i suppose you could get some kind of goggles - they make ones for cycling/running as well as swimming, or just check around the sunglass rack at a cheap store for wraparounds. Again, you have to assess your own risk and decide what works for you.
Tests is a much harder problem. I wasn't able to get free tests anywhere as a traveler. Most countries only gave them out for free to citizens or local residents with some kind of ID. Some only gave them if you claimed to have symptoms. When you're traveling overseas, especially in countries poorer than your own (which is most of them), you are going to be expected to pay for your own stuff. Or... at least that was the case till i came to Taiwan, where they give every arriving passenger on the plane two free rapid tests. Since i came back in twice, and only used one of them, i now have three. To be honest, they're really big and unwieldy and i wouldn't want to take them traveling, even though they are pretty light. I think it might be better to try to take other precautions to avoid getting sick. You should only need a test if there is an entry requirement in a particular country (most countries no longer have this requirement - already last year a lot of them were just moving to vaccination proof). If you start feeling sick, you gotta ask yourself, why do you need the test? If you're worried you might infect someone, just stay isolated for a few days and mask up if you really need to go into public. If you're worried things might get worse, then you should go to the hospital, and then they'll test you anyway. When you're traveling you don't have any requirement to go into work, so there shouldn't be any reason to have to show a positive result in order to get sick leave, or work from home, or whatever.
On the monkeypox thing... I wouldn't be too worried about that one unless you are having sex, eating game, walking around with exposed sores, etc. Although it seems it can perhaps be transmitted through the air, seems like fluids is a much more common method of transmission. If you are worried about it and you are an at-risk group in your country, you might be eligible for a free vaccine. I think MSM is considered an at-risk group in some places, for example, so check it out with your doctor or local pharmacy. Otherwise i reckon just take the normal precautions you would do for stuff like hepatatis, rabies, typhus etc.