[Essentials] Add logging

### Description

In many places within the Essentials codebase, logging is currently handled using Debug.WriteLine. While this provides basic output, it lacks the flexibility and structure needed for modern diagnostics and telemetry.

There are also several TODO comments referencing the future use of a proper logging mechanism.

This proposal suggests replacing or augmenting existing Debug.WriteLine calls with a structured logging approach using ILogger.

### Public API Changes

TBD

### Intended Use-Case

This would allow developers to:

- Filter logs by severity
- Integrate with external logging providers (e.g., App Center, Azure Monitor)
- Enable better diagnostics across platforms

This change would improve maintainability, observability, and consistency across the Essentials library.

Start by inventorying Debug.WriteLine calls and the TODO comments across the Essentials codebase, then review how ILogger could be introduced and configured across platforms. Define the public API and logging integration points before implementation. Done means the approach is agreed, logging is structured and severity-filterable, and the existing Essentials diagnostics are covered consistently.

Written by the indexing model from the issue text.