Tudor English
Why does the old Prayer Book say ‘Our Father, which art in heaven’?

I always thought it made God sound like “a thing”, a little irreverent.

“Which” is for me like hearing, for example, a Pole not putting the article in, i.e. it does not strike of good English.

“Who” was used only in questions until the middle of the 17th century. In the 16th century, “who” was only an interrogative, not a relative, pronoun. Saying “Father who art” would have been incorrect. Thus “which” had to serve for both persons and things.

The American Prayer Book of 1789 took advantage of an opportunity to update what had become an archaism.

In Early Modern English “Our father who art in heaven” risked being heard as the equivalent of contemporary English:

Dear Dad,
Who is in heaven?

A bit like the widespread misunderstanding of Psalm 121 verse 1. Early Modern English:

I will lift up mine eyes unto the hills : from whence cometh my help.

sounds to us like modern Modern English:

I will look at the hills that my help is coming from.

As if there was an army waiting in the hills to come down and win the battle for me. But a better current translation might be:

I am looking at the hills.
Where the f*ck are the reinforcements?

In other words, there are no human reinforcements, there is no army in the hills waiting to help me, I have to depend on God.

Why the relative pronoun is there

The translation favoured by the Orthodox
The last one given, which hews closely to the Greek

From the Ship.