I'm a cancer and reconstructive surgeon. The nature of my subspecialty means that I have a better working knowledge of muscle anatomy than just about any other physician or surgeon outside my subspecialty. In the deltoid, the large veins are only found on the deep aspect of the muscle where the blood supply enters the muscle (ie: the neurovascular hilum). The large vessels arborise very quickly into much, much smaller and finer branches such that nearer the muscle surface (the area where most IM injection needles would get to), there are few if any veins of sufficient size that cannulation could occur leading to an inadvertant intravenous injection. This risk is reduced further if the site is pinched during needle entry (collapses the blood vessels).
That said, I have never understood why present day training seems to advise against aspiration prior to intramuscular injection in both medical and nursing courses. Perhaps I am a bit of a dinosaur (graduated medical school in 1995), so I still do it the traditional way. I know full well that the likelihood of inadvertant IV injection with the short, fine needles (as used with Covid-19 and flu vaccination) is practically zero. However, it does no harm to aspirate, seems entirely logical and sensible; and is hardly a huge extra task in the process. I have seen enough freak events happen over my many years of work that I rather not take any chances. I also do not understand the seeming active resistance that some medical and nursing practitioners have when asked by patients to aspirate prior to IM injection. There's no need to be difficult for something so simple and if it affords the patient a measure of reassurance, surely we should just do so rather than be a**hats about it.
Sorry for my rather long post.