Revamp logger/logging

[SydneyhSmith]

We have a bunch of issues around logging to fix:

• When we look for logs, what we're expecting is never there
• The way we use the logger itself is explicitly marked as "inefficient" and wrong
• The logger values are defined in three different ways
• Most of the places we log an exception, we're not actually logging it

We should do this when we do telemetry, as part of an "observability" project.

[andyleejordan]

@JustinGrote pretty much fixed all of this. #2200