While all these ideas are logically plausible, they rest on an often unstated assumption that the brain is like a muscle - the more you work it, the stronger and healthier it is.
I have never been a linguist nor shown much aptitude but having lived in multiple countries and developed at least a passable knowledge of a couple of languages and a small capacity in a couple of more, it would indeed be nice were it true.
But all the plausible arguments about the benefits of multilingualism have been difficult to capture in empirical data. Like many fields, it is plagued by poorly designed experiments, loose data protocols, small sample sizes, non-random samples, and uncontrolled variables.
In general, the most positive assessments have come from the weakest studies. The larger and more rigorous the study, the less likely it is to find any of these results.
The most recent research follows in that pattern. From No bilingual advantage for executive function:Evidence from a large sample of children in theAdolescent Brain and Cognitive Development(ABCD) Study. by Anthony Steven Dick, et al. From the Abstract:
Learning a second language in childhood is inherently advantageous for communication. However, parents, educators, and scientists have been interested in determining whether there are additional cognitive advantages. One of the most exciting, yet controversial1findings about bilinguals is a reported advantage for executive function. That is, several studies suggest that bilinguals perform better than mono-linguals on tasks assessing cognitive abilities that are central to the voluntary control of thoughts and behaviors—-the so-called “executive functions” (e.g., attention, inhibitory control, task switching, and re-solving conflict). Although a number of small-sample studies have reported a bilingual executive function advantage (see for review), there have been some failures to replicate, and recent meta-analyses have called into question the reliability of the original empirical claims. Here we show, in a very large demographically representative sample (N=4524) of 9-10-year-olds across the United States, that there is little evidence for a bilingual advantage for inhibitory control/attention and task switching/cognitive flexibility, which are key aspects of executive function. We also replicate previously-reported disadvantages in English vocabulary in bilinguals. However, these are substantially mitigated when we account for individual differences in socioeconomic status or intelligence. In summary, notwithstanding the inherently positive benefits of learning a second language in childhood, we found little evidence that it engenders additional benefits to executive function development.