Whether it is a positive or negative, sitting with classmates who are much older, really is highly individual to the child, family, and school systems. My own experience with skipping multiple grades in math midyear was first, at a similar age to OPs DC, and second, a few years later. The first time, I believe I went up two grades midyear, on a school change and grade skip. On this occasion, I placed into a mixed-age classroom. I don't remember any noticeable social effects specific to the skip, probably because the school model was ability grouped/mixed age departmentalized classes.
The second time, I was a two-whole-grade-equivalent skipped seventh-grader, additionally SSA into algebra II. I had something like pre-algebra the previous year, independent studied (not sure what, TBH) the first few weeks of seventh grade, then sat in an algebra I class for, I think, a chapter or two, and finally ended up in algebra II/trig, in a class of 11th and 12th graders, who were probably six to eight years older than I was. This worked out for me, without being any worse off socially, I don't think, than I would have been staying with my age/grade peers. Of course, I also had the benefit of a MS/HS joint campus, very accommodating school administrators, and savvy and persistent parental advocacy. And an unusually warm, accepting school climate.
So it can happen. Though more often one must choose the least-worst solution. Or prioritize particular downsides.
