The US BLS has 6 different unemployment measures. The one that's usually quoted is U-3 which means unemployed but seeking work. But if you left the country, I assume you're not counted in any unemployment measurement. (Though I also assume that's a sufficiently unusual edge case that it doesn't really move the needle on any of the statistics.)
In the US, you're not "unemployed" if you don't have a job and you don't want one.
I believe if you're a US citizen vacationing long-term in France because your work prospects aren't great at the moment - you'll still show up as not in the labor force in the labor force participation rate: https://fred.stlouisfed.org/series/CIVPART
But you won't show up in u-1 through u-6.
> Discouraged workers (U-4, U-5, and U-6 measures) are persons who are not in the labor force, want and are available for work, and had looked for a job sometime in the prior 12 months
In general, it doesn't really make sense to count someone who isn't trying to be employed as unemployed in general. I am not sure how you would distinguish between a 60 year old who decided they had plenty of money and would rather not work for someone any longer and a 60 year old who got laid off and can't find anyone to hire them for the work they are trained to do.
And, as you say, there are labor force participation numbers if that's what you're interested in.
Maybe I haven't been reading too closely and have missed the answer, but how many of the laid off employees were on work visas that are now also looking at having to leave the country? Since it's tech companies, I'd assume there's a decent percentage. How do those types of numbers affect the unemployment stats?
I expect that if you combine the percentage of H1Bs at tech companies, the percentage of layoffs in tech overall, and the percentage of that number who can't find something else and have to or choose to leave the country you end up with a fairly modest number in the scheme of things.