Mm. I'm a bit sceptical of the historical expertise of someone who thinks that "Who art Henry" is 19th century language. (It's not actually grammatically correct English from any century whatever: "art" is the second person singular, so this is like saying "who are Henry?")
Yes, I've read the History of Redemption by Edwards, The Pilgrim's Progress and Holy War by Bunyan, quite a few Spurgeon sermons, and Holiness by Ryle in addition to (parts of) his commentaries on the gospels. I also read the puritans - I read Thomas Brook's Precious Remedies Against Satan's Devices and the Body of Divinity (Thomas Watson) last year.
Lately I've read a few older biographies/autobiographies - Thomas Scott's autobiography (The Force of Truth), Halyburton's autobiography, and James Henley Thornwell and Benjamin Morgan Palmer biographies.
Right now I'm reading the Life and Times of Jesus Messiah by Alfred Edersheim (19th century).
"Who art Henry?" was never grammatical English. "Art" was the second person singular present form of "to be" and it was already archaic by the 17th century. "Who is Henry?" would be fine.
In some languages you can put a second person conjugation next to a noun that might otherwise use third person verbs, and it serves as implying that you are that noun. I'm not sure if older forms of English had that construct. I think many Indo-European languages do.
The part of the lord's prayer that says "our father who art in heaven" is kinda like this - father is linked to a second person conjugation. You could remove some words and make it into "father art in heaven", which you claim is ungrammatical. I'm skeptical that it was.
“who art in heaven” is a grammatical relative clause because the subject of the verb is the relative pronoun “who” which is second person in that context. You can still get this kind of thing in modern English, for example “I, who am a farmer, will be happy” is grammatical because the relative pronoun “who” is first person there. That doesn’t mean it would be grammatical to say “*A farmer am happy” and it wouldn’t have worked with art either.
Conceivably it’s grammatical if Henry is vocative and the pronoun is dropped colloquially, like “Who art [thou], O Henry?” but it’s a stretch.
I think the further back you go in Indo-European grammar, the more common the thing you are describing becomes. For me it's less of a question of if English did this, and more like how far back you need to go.
Today, even ignoring the dated conjugation, "who art in heaven" or "who are in heaven", does not make sense. We would switch it into the third person.
The problem is the subjunctive mood of the word "art".
"Art thou" should be translated into modern English as "are you to be", and so works better with things (what are you going to be), or people who are alive, and have a future (who are you going to be?).
Those are probably the contexts you are thinking of.