Is "soul-to-soul talk" a common expression in English?

The common English expression is "heart-to-heart talk", or even just "a heart-to-heart".

Other similar expressions, like "soul-to-soul", while not common, would probably be understood as a reference to or variation of "heart-to-heart".

A phrase that comes to mind to use for "soul to soul" is "personal, deep and meaningful", which I first heard in the 1980's.

Google Ngrams doesn't find "personal deep and meaningful" as a complete phrase, but does show a rise in usage of "deep and meaningful" continuing from about 1920 to the present.

Hence "Personal, deep and meaningful" is probably tautological to some degree, with "deep and meaningful" more often used on its own:

To have deep and meaningful conversations is to talk about mental and spiritual things. {mindreality.com}

Used to describe a conversation of great emotion (usually, but not exclusively describes a conversation of a sad nature). {Urban Dictionary}

However, if the purpose of the conversation is to attempt to reconcile a point of contention between two people, "heart to heart" would be more idiomatic, as for example in "I think you and I need to have a heart to heart (talk) about this".