Add Content-Type header to Agent responses

[simonmarty]

• Add Content-Type header

Issue #, if available:

Description of changes:
Useful for pretty-printing agent responses in browsers and API test tooling.

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.

[codecov-commenter]

Codecov Report

❌ Patch coverage is 78.08219% with 16 lines in your changes missing coverage. Please review.
✅ Project coverage is 41.99%. Comparing base (4e08f07) to head (e836a37).
⚠️ Report is 11 commits behind head on main.

Files with missing lines	Patch %	Lines
aws_secretsmanager_agent/src/server.rs	76.92%	9 Missing ⚠️
aws_secretsmanager_agent/src/main.rs	40.00%	3 Missing ⚠️
...nager_caching/src/secret_store/memory_store/mod.rs	33.33%	2 Missing ⚠️
aws_secretsmanager_agent/src/cache_manager.rs	0.00%	1 Missing ⚠️
aws_secretsmanager_agent/src/config.rs	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #80      +/-   ##
==========================================
+ Coverage   41.71%   41.99%   +0.27%     
==========================================
  Files          14       14              
  Lines        8567     8534      -33     
==========================================
+ Hits         3574     3584      +10     
+ Misses       4993     4950      -43     

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