fix: support Anthropic reasoning budgets for Bedrock application inference profile ARNs (#17755)

## Background

Anthropic reasoning budgets were ignored for Bedrock application
inference profile ARNs, producing text without reasoning and an
unsupported-option warning.

## Root Cause

Anthropic detection relied solely on modelId containing "anthropic";
opaque application profile ARNs lack that marker, which was confirmed by
the omitted thinking request field and budgetTokens warning.

## Summary

Application inference profile ARNs with an Anthropic-only reasoning
budget are now handled as Anthropic models. Reproduction artifacts were
removed and a patch changeset was added.

## Testing

Added behavior-based regression coverage verifying the thinking request
field, parsed reasoning output, and absence of the budgetTokens warning.

## End-to-end Validation

- `pnpm -C packages/amazon-bedrock exec tsx live-profile-validation.ts`
— created a temporary live Claude Sonnet 4.5 application inference
profile, received reasoning with no warnings, and deleted the profile.

## Related Issues

Fixes #11035

Closes #17716

Co-authored-by: maksimyaromin
<15309257+maksimyaromin@users.noreply.github.com>

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Co-authored-by: ai-sdk-factory <308175966+ai-sdk-factory@users.noreply.github.com>
Co-authored-by: Aayush Kapoor <83492835+aayush-kapoor@users.noreply.github.com>