chore: do not use internal append in ToString instances for basic types

[TwoFX]

This PR shifts some material in Init to make sure that the ToString instances of basic types don't rely on String.Internal.append.

[mathlib-lean-pr-testing]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase a32be44f909683a2f5dff4bb955dfa986bbc9b1c --onto e8048291010c815d0d30926924e7ad7afc18b1c0. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-11 15:33:44)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase a32be44f909683a2f5dff4bb955dfa986bbc9b1c --onto ff6816a854ef5cf2966519452d03933785f2fdeb. You can force reference manual CI using the force-manual-ci label. (2026-03-11 15:33:46)