Separate shell profile setup from broader environment-configuration logic in dotnetup init

## Summary

Follow-up from #53447 and #53909.

The init/install/default-install flow has accumulated overlapping responsibilities around shell profile editing, PATH / DOTNET_ROOT mutation, and the meaning of InstallType. We should do a focused cleanup pass once the current PRs settle.

## Proposed work

- separate profile modification from broader environment/system configuration behavior
- clarify the naming and responsibilities of ShouldReplaceSystemConfiguration, ApplyEnvironmentModifications, and related helpers
- revisit how InstallType is used so it reflects the right concept consistently
- simplify the Windows/Unix branching in DotnetEnvironmentManager and the init workflow
- decide which behavior belongs in init, defaultinstall, and normal install commands

## Related

- #53447
- #53909