[Off-chain] fix: duplicate log fields

[bryanchriswhite]

Summary

Construct a new logger instance for each session during settlement to avoid field duplication.

Issue

• https://discord.com/channels/824324475256438814/1316109400917934201/1330007345882988665

Type of change

Select one or more from the following:

• New feature, functionality or library
• Consensus breaking; add the consensus-breaking label if so. See [Infra] Automatically add the consensus-breaking label #791 for details
• Bug fix
• Code health or cleanup
• Documentation
• Other (specify)

Testing

• Documentation: make docusaurus_start; only needed if you make doc changes
• Unit Tests: make go_develop_and_test
• LocalNet E2E Tests: make test_e2e
• DevNet E2E Tests: Add the devnet-test-e2e label to the PR.

Sanity Checklist

• I have tested my changes using the available tooling
• I have commented my code
• I have performed a self-review of my own code; both comments & source code
• I create and reference any new tickets, if applicable
• I have left TODOs throughout the codebase, if applicable