Replace custom logger with tslog

[JustinGrote]

Prerequisites

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Summary

Prerequisite to: #4441

To implement this feature, this is an opportune time to look at taking a dependency on a proper logging system to allow for more sinks and a more robust operation.

Proposed Design

I have a lot of love for tslog, which is extremely extensible and can be tied into the existing methods to avoid breaking changes.

@andschwa would you have an appetite for taking this dependency or would you prefer to just overhaul the existing implementation?

[andyleejordan]

I'd be totally fine with tslog, it looks nice! Just want to point out that for #4441 we have to wait until our engine is updated to 1.76...and we're a long way from that at 1.67.0. We are tied to the version that Azure Data Studio uses, so don't expect it to change quickly!