How to prevent dry chicken in soup?
Don't cook the chicken pieces for so long. Add them ten or twenty minutes before serving. For that matter, I wouldn't simmer the aromatics for that long either.

Do the long simmer and cooking to make the chicken stock, then strain the now-tasteless and mushy expended bits from the flavorful stock. Heat the stock and add the sweated veggies, diced chicken, and any pasta/rice/dumplings desired but only cook briefly before serving.