New International Version
Whoever is kind to the poor lends to the LORD, and he will reward them for what they have done.
And if anyone gives even a cup of cold water to one of these little ones because he is My disciple, truly I tell you, he will never lose his reward."
Jesus confirmed it in Matthew 25:
And the King will reply, 'Truly I tell you, whatever you did for one of the least of these brothers of Mine, you did for Me.'
The two Matthew passages together provide support to the Proverbs passage that connects the LORD with Jesus. See the bolded words for the linkage.
Jesus encouraged us to be quick to believe in Luke 24:
25 He said to them, “How foolish you are, and how slow to believe all that the prophets have spoken! 26Did not the Messiah have to suffer these things and then enter his glory?” 27And beginning with Moses and all the Prophets, he explained to them what was said in all the Scriptures concerning himself.
Is Matthew 25:40 establishing Proverbs 19:17 is a 'prophecy' about Jesus being King YHVH?
Not by Matthew 25:40 alone but with Matthew 10:42 together. Then yes.