[refactor] Combine the ToString and ToPrivateString implementations

Summary:
This is a partial backport of Core PR14646 : https://github.com/bitcoin/bitcoin/pull/14646/commits/1eda33aabc15b905a1e23ffab648ecf2a8f5322b

Depends on D6195

Test Plan:

ninja all check-all

Reviewers: #bitcoin_abc, majcosta

Reviewed By: #bitcoin_abc, majcosta

Subscribers: majcosta

Differential Revision: https://reviews.bitcoinabc.org/D6196