MicroShift is a Taiwanese company, I think founded in the '80s as part of the country's broader industrialization. I can't find any evidence of it having been bought out by SRAM.
MicroShift indeed produces more budget oriented components than SRAM, more comparable to Shimano's lower end like Tiagra and that level of gravel/mountain stuff. I have MicroShift trigger shifters that I got to replace the original twist shifters on my commuter hardtail MTB. They work fine for a bike that I expect will be stolen someday, their performance is solidly in line with their price point.