Coronavirus booster shots covering BA.5 may be little more than a month off, but Dr. Anthony Fauci says his retirement is far more distant. Fauci, the chief medical adviser to President Joe Biden, gave the positive diagnosis of the vaccine development — and his own professional longevity — this week as COVID hospital admissions climbed, driven by the new viral variant. BA.5, the ultra-contagious and now-dominant omicron COVID subvariant, has been charging across America throughout the summer. In New York City, test positivity rates have stayed in double digits for more than a month, according …