Refactor shared solver to use theory builtin inference manager (#6960)

Refactor shared solver to use theory builtin inference manager (#6960)

This ensures that e.g. COMBINATION_SPLIT shows up under theory::builtin::inferencesLemmas, and -t im. It also removes outdated interfaces from OutputChannel, and makes the feature TheoryEngine::ensureLemmaAtoms more modular, which was required for making these interfaces more consistent.

It also ensures that TheoryBuiltin has an inference manager, which will simplify special casing in #6956.