You can look at studies like https://www.tandfonline.com/doi/pdf/10.1080/1331677X.2022.20... if you want to look at those multi-causal aspects. In general however, demographics with higher socioeconomic status has lower crime rate and the concept is well established (https://pmc.ncbi.nlm.nih.gov/articles/PMC7820585/).

A missing aspect with immigration when it comes to statistics is time spent in the country. The likelihood that a person has ever committed a crime in a specific country is generally lower the less time they spend in that country, especially as that number reach zero. The apple to apple comparison would be to look at the average person of average age, in any specific demographic, and ask if they have ever committed a crime, which is not the same as committed a crime in a specific country. That would be the crime rate. An other way would be to ask the question regarding a given year, what is the probability of an individual to commit a crime. The rate of the average person lifetime will not align with the rate of any given year.

The relation between crime and socioeconomic has been thoroughly debated and research when it comes to race, with the finding that race is not related to violent crime, but only once socioeconomic factors (and other related aspects) has been controlled for. If you disregard socioeconomic factors, then race has a distinct relation with violent crime. It is only because researchers control for related factors that we get the findings that we get.

People can disagree with studies should be valid and which doesn't, or look at different meta studies and say which ones is more valid than the others, but I would recommend that one engage with the discussion rather than throw around assumptions about assumptions.