Enable Loggers to retrieve run-time state of LoggingService to configure their own behaviors

It is very odd that loggers like BinaryLogger need to set environment variables and change the Traits' state. There are two aspects of logger configuration that need coordination:

* _requirements_ of the various loggers - for example, TerminalLogger and BinaryLogger both need Target outputs to be enabled. The presence of either of those loggers should cause the LoggingService to force that feature to enabled
* _optional behaviors_ of various loggers - for example, the Console logger checks the Traits to see if it should render specific kinds of additional data

I think we have a mismatch here that needs two things to happen to fix it:
* The requirements from the first category are not uniformly enforced by the LoggingService configuration/initialization. To fix this we need to push more logic into the BuildParameters and friends.
* The optional features from the second category are not _communicated_ to the loggers at their run-time. They are forced to read the Traits, which are mutable and may not be kept up to date as other components change them. To fix this, we need a way to communicate the various flags on the LoggingService (but probably not through that LoggingService directly) at run-time to the Loggers - probably through Initialize?

_Originally posted by @baronfel in https://github.com/dotnet/msbuild/pull/12082#discussion_r2254530081_