fix(instrumentation-py): repair BeeAI, Braintrust, and Burr OTel 2.x spans

[Nightingalelyy]

Summary

• repair BeeAI error handling so one rejected model request produces one failed chat span, preserve provider status without false completion usage, and retain direct-chat assistant output
• merge Braintrust evaluation metadata with propagated Respan context so scores, metrics, tags, and log IDs remain platform-visible
• promote Burr action failures to the application workflow and retain custom and bounded stream lifecycle metadata
• add focused regressions and one patch release intent covering all three Python instrumentation packages

Release Intent.

• .release-intents/20260816-python-beeai-braintrust-burr-tracing.json
• patch: respan-instrumentation-beeai
• patch: respan-instrumentation-braintrust
• patch: respan-instrumentation-burr

Validation

• I updated or added a .release-intents/*.json file if this PR changes a release-managed package

• I ran the relevant local checks for the packages I touched

• BeeAI: 12 tests passed

• Braintrust: 4 tests passed

• Burr: 8 tests passed

• release intent validation passed

• clean wheels built and were force-installed from local file URLs

• exact MCP marker otel2-fix-py-group-10-20260816T071856Z: 12/12 trace trees and 33/33 full span records inspected, with no duplicate or orphan spans

• Full source and paired-example diffs were audited against every applicable document under contribution/; canonical span fields, OTel attribute shapes, release-intent/version ownership, and package boundaries have no remaining package-owned violation.

External follow-ups

• None documented.

Companion examples

• fix(examples-py): validate BeeAI, Braintrust, and Burr OTel 2.x spans respan-example-projects#58

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