Excel

gistfile1.txt

=LET(
  src, FILTER(A2:C1000, A2:A1000<>""),
  REDUCE(
    {"ID","QuarterStart"},
    SEQUENCE(ROWS(src)),
    LAMBDA(acc,i,
      LET(
        id, INDEX(src,i,1),
        st, INDEX(src,i,2),
        en, INDEX(src,i,3),

        qs, DATE(YEAR(st), INT((MONTH(st)-1)/3)*3+1, 1),
        qe, DATE(YEAR(en), INT((MONTH(en)-1)/3)*3+1, 1),

        n, 1 + INT(DATEDIF(qs, qe, "m")/3),
        qlist, EDATE(qs, SEQUENCE(n,1,0,3)),

        block, HSTACK(MAKEARRAY(n,1,LAMBDA(r,c,id)), qlist),
        VSTACK(acc, block)
      )
    )
  )
)

=LET(
q, TOROW(E2:E100,1),
u, SORT(UNIQUE(q)),
HSTACK(u, COUNTIF(q, u))
)