Jesus prays in Gethsemane, and the Father sends an angel to strengthen Him.

That means prayer time is over, right?  The angel soothes Him.

Not for Jesus.  Jesus begins to pray so intensely that he sweats blood, and this happens after the angel comes.

Angels don’t come to end prayer.  They come to strengthen us for even more intense prayer.  So too the Angel-Spirit, who prays along with us with groans that cannot be uttered.