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!

[EdgarModesto23]

Hello @Standing-Man . Thank you for your contribution! I left a message on the original issue with some concerns I have. TL;DR: I haven't been able to reproduce the issue described. If you'd like to, I prepared a repository that can help you test this end-to-end and see the difference between master and your changes. If you do, please make sure to post your results here! I'll be more than glad to approve your changes if you find it's affecting master as described