refactor(api): fix eslint warnings

[chancancode]

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Which problem is this PR solving?

Fixes the following eslint warnings:

    /home/runner/work/opentelemetry-js/opentelemetry-js/api/src/diag/ComponentLogger.ts
      36:25  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any
      40:25  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any
      44:24  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any
      48:24  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any
      52:27  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any
      60:9   warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any

    /home/runner/work/opentelemetry-js/opentelemetry-js/api/src/experimental/trace/SugaredTracer.ts
      80:5  warning  'context' is already declared in the upper scope on line 17 column 10  @typescript-eslint/no-shadow
      129:5  warning  'context' is already declared in the upper scope on line 17 column 10  @typescript-eslint/no-shadow
      135:5  warning  'context' is already declared in the upper scope on line 17 column 10  @typescript-eslint/no-shadow

    /home/runner/work/opentelemetry-js/opentelemetry-js/api/src/trace/NoopTracer.ts
      102:37  warning  Unexpected any. Specify a different type  @typescript-eslint/no-explicit-any

Ref #5365

Fixing TextMapPropagator.ts is a breaking change, so that will be submitted separately.

Short description of the changes

Refactor to avoid the patterns being flagged.

Type of change

Please delete options that are not relevant.

• [ ] Bug fix (non-breaking change which fixes an issue)
• [ ] New feature (non-breaking change which adds functionality)
• [ ] Breaking change (fix or feature that would cause existing functionality to not work as expected)
• [ ] This change requires a documentation update

How Has This Been Tested?

Please describe the tests that you ran to verify your changes. Provide instructions so we can reproduce. Please also list any relevant details for your test configuration

• [x] TypeScript

Checklist:

• [x] Followed the style guidelines of this project
• [ ] Unit tests have been added
• [ ] Documentation has been updated

[codecov[bot]]

Codecov Report

:white_check_mark: All modified and coverable lines are covered by tests. :white_check_mark: Project coverage is 95.01%. Comparing base (93187f0) to head (ffcf8cc). :warning: Report is 29 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #5366      +/-   ##
==========================================
- Coverage   95.01%   95.01%   -0.01%     
==========================================
  Files         303      303              
  Lines        7946     7945       -1     
  Branches     1607     1607              
==========================================
- Hits         7550     7549       -1     
  Misses        396      396              

Files with missing lines	Coverage Δ
api/src/diag/ComponentLogger.ts	94.73% <100.00%> (-0.27%)	:arrow_down:
api/src/experimental/trace/SugaredTracer.ts	87.23% <100.00%> (ø)

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[github-actions[bot]]

This PR is stale because it has been open 60 days with no activity. Remove stale label or comment or this will be closed in 14 days.

[github-actions[bot]]

This PR is stale because it has been open 60 days with no activity. Remove stale label or comment or this will be closed in 14 days.

[opentelemetrybot]

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