[RFC] Use Tracing For Solver Logs/Output

[rydrman]

Background and Problem Space

Our current solver prints output directly via a custom output handler.

Proposal

Instead, the two could be separated by the tracing abstraction where the solver emits events with structured fields and then a separate subscriber receives and process those events as required. This would improve our ability to control this output and avoid the propagation of verbosity levels etc. We could further leverage these trace events and spans to pull additional timing and progress insights out without tying ourselves to a single subscriber/output format.