refactor: move logger interface to types

[mtsitrin]

PR Standards

Opening a pull request should be able to meet the following requirements

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Close #XXX

<-- Briefly describe the content of this pull request -->

For Author:

• Targeted PR against correct branch
• included the correct type prefix in the PR title
• Linked to Github issue with discussion and accepted design
• Targets only one github issue
• Wrote unit and integration tests
• All CI checks have passed
• Added relevant godoc comments

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For Reviewer:

• confirmed the correct type prefix in the PR title
• Reviewers assigned
• confirmed all author checklist items have been addressed

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After reviewer approval:

• In case targets main branch, PR should be squashed and merged.
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[mtsitrin]

The only change here is that syncCache removed as it's not used.
grouping and comments other than that

[codecov]

Codecov Report

Attention: Patch coverage is 71.25000% with 23 lines in your changes are missing coverage. Please review.

Project coverage is 44.05%. Comparing base (6406c2e) to head (a4fda42).
Report is 1 commits behind head on main.

❗ Current head a4fda42 differs from pull request most recent head 6823fe8. Consider uploading reports for the commit 6823fe8 to get more accurate results

Files	Patch %	Lines
settlement/dymension/dymension.go	65.45%	13 Missing and 6 partials ⚠️
settlement/grpc/grpc.go	0.00%	2 Missing ⚠️
da/celestia/mock/server.go	0.00%	1 Missing ⚠️
da/grpc/grpc.go	0.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #633   +/-   ##
=======================================
  Coverage   44.04%   44.05%           
=======================================
  Files         120      120           
  Lines       16531    16549   +18     
=======================================
+ Hits         7281     7290    +9     
- Misses       8219     8224    +5     
- Partials     1031     1035    +4     

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The base branch was changed.