I'm in an EU country and it's really rare to see a company do any background checks at all. Be honest, if/when you're asked about it of course - but just from personal anecdotal experience, it's rare that somebody even bothers to ask. (this might vary of course from country to country)
another country is very unlikely to let someone immigrate (or even visit) with a criminal record
I have a squeaky clean record, was driving an 8 year old toyota camry at the time, and by all accounts appeared as the most boring non-offensive person out there trying to cross the Vancouver border with my mom and sister (who were both US citizens by then too, so it isn’t like I was transporting non-citizens across the border) for a daytrip during a weekend. And CBP went on a 10-15 mins long line of questioning about what exactly I do for work (was in a somewhat niche area of MSFT at the time, so it isn’t like they would be suspicious of the employer being shady or anything like that, but also it was really difficult to explain exactly what i do for work to someone who sounded like they just discovered the existence of software engineering and have zero idea what any of it is). Only after that got cleared up and answering a few more strangely personal questions (from me, as well from my mom and sister), they let me in. For context, they were visiting me from GA, and I was the driver. The entire process took close to 20 mins. And something similar happened at least every other time I tried to cross the WA-Vancouver border.
In contrast, crossing the border back into the US was as smooth and efficient as I could have possibly imagined every single time. Despite my passengers occasionally creating non-happy-path situations for crossing the border. On that same trip I mentioned above, my mom decided to buy some really nice looking grapes and bring them back home (which was not known to me at the time). The US officer, as we were crossing the border back into the US, asked if we were bringing anything back. My mom honestly said “oh, nothing, except these grapes.” Unknown to us, those grapes were considered invasive/harmful species that weren’t allowed to be brought into the US. All that did was adding less than an extra minute to our trip, because the border officer just calmly explained to us the situation, profusely apologized, and said that our options were to either eat the grapes or watch as he throws them away into a trash can in front of us. The whole experience from start to finish took less than 2 minutes.
P.S. Major apologies for going on a massive side-tangent. All I wanted to say was that, yeah, with any sort of a criminal record (even as minor as a misdemeanor), a lot of international options are almost instantly axed at the visa stage. Way before even getting to the “will the employer be ok with my criminal record” stage.