Hast vs. Has

'Hast' is the archaic form of 'has', and is no longer used except poetically or for historical effect. Lewis Carroll's '. . .And hast thou slain the Jabberwock?' is the most recent example I can think of.

I have, thou hast, he/she/it hath
we have, you/ye have, they have

Hast thou seen thy friend of late?
Hath he seen his friend of late?

Not part of modern English, of course.

I would dispute the assertion that 'hast' isn't part of 'modern English'. It is still used in dialect in some parts of England, & also by certain religious communities.

'Jabberwocky' is by no means the word's most recent appearance in literature. For instance, it was used several times in Ezra Pound's Pisan Cantos (1948).

I'm not sure 'hast' can be described as a form of 'ha

True, it may be used in a few English dialects, but it is not exactly common useage and in those cases is a remnant from another age.

I would advise the use of 'hast' only in a poetic sense by non-native speakers, and then with care.

On the contrary, 'hast' is part of the living language in northern England, and very commonly used in some regions.

I would say that if a word has an unbroken history of everyday use, it can no more be described as a 'remnant from another age' than words such as 'give' and 'take'. (Though in another, non-derogatory sense, I suppose most of the words we use are 'remnants of other ages'.