How can the principle of "certainty is not removed by doubt" be reconciled with the Prophetic narrations that forbid dipping one's hand into a vessel before washing it upon waking from sleep, and command ablution for one who has slept, even though both are based on doubt concerning purity?

The two hadiths do not contradict the principle that the default state of water is purity and the default state of the hand is purity. The first hadith (definition), which prohibits dipping the hand into a vessel before washing it, is interpreted as a recommendation (tanzīh), not a prohibition (taḥrīm). The majority of scholars hold that if one violates this and dips their hand, the water is not spoiled, nor is the dipper sinful. As for the second hadith, scholars differ regarding whether sleep invalidates ablution. The preponderant opinion is that the sleep of one who is sitting firmly grounded does not invalidate ablution.