Welcome!
I think you will find that, although there is always space for exceptions even to the exceptions, the consensus anecdotally and professionally is generally to address asynchronous (whether simply for developmental reasons, or more persistent learning differences/disabilities) skill areas separately. IOW, if she is doing well, even possibly underchallenged, academically, then one should not repeat/hold her back for behavioral reasons--especially behaviors that are explicitly tied to her identified disability. Note that there is no guarantee that an additional year in first grade will make those behaviors vanish, if they are truly associated with a sensory processing disorder. In fact, repeating may add other behaviors, as her academics become a poorer match, which children often communicate through their behavior.
In the hypothetical, it is possible that holding her out for another year of play-based kindergarten (if such she was in) might have been a consideration at the time, but the reality is that that did not happen, and she has now had a year of academic first grade, so retaining her now would be a very different proposition. In any case, retention/delayed entry research finds very few long-term positive outcomes to retention in situations other than when students had restrictions in access to formal instruction (prolonged medical absences, displaced persons in settlement camps, etc.). Outcomes data is somewhat positive in the short-term (approx one to two years), but overwhelmingly neutral to slightly negative in the long term (approx six or more years). And this is including neutral outcomes that actually mean the student is one year behind their age peers academically (due to lack of that one additional year of instruction).
On a personal level, our #1 was a very wriggly, impulsive small person, then demonstrating end of first grade/beginning of second grade achievement, for whom we convinced our tiny private school to allow early entrance to first grade directly from preschool (no kindergarten). The lower school head was specifically concerned about behavior, maturity, and missing out on play (although the kindergarten was an academic full-day kindergarten, so not that much additional play), but our contention was, knowing our own child, the likelihood was that the active-impulsive-overly chatty behaviors would increase with a greater instructional mismatch--and less mature peer models. We were already placing academically into a level about a year below DC's true instructional level. (This was by design, though; as I've discussed elsewhere, my family has historically underplaced instructionally about 1-1.5 grade levels on grade skips, as a means of balancing instructional needs, executive function demands, and social skills considerations.) Sure enough, the underlying active-impulsive traits have never really gone away, although they are now, many years later, under generally excellent self-management. Even the lower school head acknowledged by the end of that year that kindergarten would have been a mistake.
And to the school's conclusion that she is not bored now, I would be curious as to the data they used to determine that.
