Reduce default logger usage (#23030)
### Description
<!-- Describe your changes. -->
We have use cases where multiple sessions are created concurrently.
Minimizing the usage of the default logger is important for these
scenarios.
Wire through the session logger to as many places as possible. The EP
logger can also be used once the session is created (can't be used
during EP construction/kernel registration but can be used in
GetCapability and Compile).
### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->
Improve logging when there are concurrent sessions.
