feat: add logger to packager.Publish

[mkcp]

Description

This one ended up being really simple because most of the downstream code had already been ported to slog. I started updating the tests to use the new logging, but decided that it's better if we wait until we swap over to the default format. Added a couple review comments for discussion.

Related Issue

Relates to #2576

Checklist before merging

• Test, docs, adr added or updated as needed
• Contributor Guide Steps followed

[netlify]

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[codecov]

Codecov Report

Attention: Patch coverage is 0% with 9 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/pkg/packager/publish.go	0.00%	9 Missing ⚠️

Files with missing lines	Coverage Δ
src/pkg/packager/publish.go	0.00% <0.00%> (ø)

... and 3 files with indirect coverage changes

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