Are tears during Salatul-Istikhara, coupled with a sense of relief and comfort regarding the matter, a sign that the Istikhara is sound?

If your heart feels at ease after performing Istikhara, then proceed with the matter for which you sought guidance. Crying during the Istikhara prayer may be due to the heart's attachment to the matter and a strong desire for it to occur, and this does not affect the validity of the Istikhara or the prayer itself.