fix(sdk): error callback should await shard flush on producer shutdown

[haubur]

Which issue does this PR address?

Closes #3947

Rationale

On shutdown() the IggyProducer calls the shutdown() method of the Dispatcher which broadcasts
a termination signal to it's workers. This immediately breaks the loop of the error callback task, which then
does not receive any errors from the final flush anymore.

What changed?

The error callback task does not receive the stop signal anymore. The channel is still open,
and shards can put errors in the queue. On join in shutdown() (after shard tasks are joined) the
error callback is awaited for as long as the queue is emptied.

Local Execution

• Passed
• Pre-commit hooks ran

AI Usage

Test proposed by Claude code.

[github-actions]

Thanks for the PR. It is labeled S-waiting-on-review and queued for review.

Slash commands (own line, regular comment) move it around the queue:

• /ready - back to S-waiting-on-review after addressing feedback
• /author - flip to S-waiting-on-author while you finish changes
• /request-review @user-or-team - request a reviewer

See CONTRIBUTING.md for details.

[codecov]

Codecov Report

❌ Patch coverage is 95.08197% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.82%. Comparing base (4c475df) to head (f555aa7).

Files with missing lines	Patch %	Lines
core/sdk/src/clients/producer_dispatcher.rs	95.08%	1 Missing and 2 partials ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##             master    #3953       +/-   ##
=============================================
- Coverage     84.03%   69.82%   -14.21%     
  Complexity     1358     1358               
=============================================
  Files          1215     1215               
  Lines        170548   146058    -24490     
  Branches     138292   113800    -24492     
=============================================
- Hits         143315   101984    -41331     
- Misses        23381    40181    +16800     
- Partials       3852     3893       +41     

Components	Coverage Δ
Rust Core	66.56% <95.08%> (-18.37%)	⬇️
Java SDK	66.67% <ø> (ø)
C# SDK	74.96% <ø> (ø)
Python SDK	90.13% <ø> (ø)
PHP SDK	84.48% <ø> (ø)
Node SDK	95.83% <ø> (+0.02%)	⬆️
Go SDK	68.29% <ø> (ø)

Files with missing lines	Coverage Δ
core/sdk/src/clients/producer_dispatcher.rs	94.60% <95.08%> (+0.63%)	⬆️

... and 319 files with indirect coverage changes

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[haubur]

/ready