MAINT: Fixing deprecated usage

[rlundeen2]

• Added print_deprecation_message (updated from an unused method)
• Updated inconsistent log warnings to use this. It allows us to easily see warnings in tests, because previously we often did logger.warn
• Went through and fixed all deprecated usage in tests and classes, other than those tests that were explicitly testing they existed

There are some flaky tests, but those are fixed in #1304; I want to merge that first

The journey was from something like 100 warnings originally -> 24 warnings -> 100 warnings when I explicitly called warn -> 30 warnings

[jsong468]

Looks good!