fix(connector): extract dynamic route field as raw JSON string

[Standing-Man]

Which issue does this PR close?

Closes #3177.

Rationale

What changed?

Local Execution

• Passed / not passed
• Pre-commit hooks ran / not ran

AI Usage

[codecov]

Codecov Report

❌ Patch coverage is 73.33333% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 18.03%. Comparing base (5e98ec9) to head (7bb2856).

Files with missing lines	Patch %	Lines
...rs/sinks/iceberg_sink/src/router/dynamic_router.rs	73.33%	8 Missing ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##             master    #3256       +/-   ##
=============================================
- Coverage     73.84%   18.03%   -55.81%     
  Complexity      943      943               
=============================================
  Files          1193     1191        -2     
  Lines        108970    94715    -14255     
  Branches      85985    71745    -14240     
=============================================
- Hits          80471    17085    -63386     
- Misses        25764    77238    +51474     
+ Partials       2735      392     -2343     

Components	Coverage Δ
Rust Core	0.45% <73.33%> (-74.46%)	⬇️
Java SDK	60.14% <ø> (ø)
C# SDK	69.38% <ø> (-0.08%)	⬇️
Python SDK	81.43% <ø> (ø)
Node SDK	91.53% <ø> (+0.21%)	⬆️
Go SDK	39.80% <ø> (ø)

Files with missing lines	Coverage Δ
...rs/sinks/iceberg_sink/src/router/dynamic_router.rs	30.13% <73.33%> (+30.13%)	⬆️

... and 682 files with indirect coverage changes

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[hubcio]

@EdgarModesto23 mind taking a look at this one? it's iceberg-related. thanks!