fix(producer): pass variables to duration probe

[miguel-heygen]

Summary

• pass render variable overrides into the browser session used for duration discovery
• keep duration derivation and frame capture on the same variable state
• add regression coverage at the producer probe boundary

Reproduction

Confirmed on published 0.7.56: render --variables {"short":true} exposed the value during capture but duration discovery used the default state, producing 240 frames / 10s instead of 48 frames / 2s at 24fps.

Tests

• bun test packages/producer/src/services/render/stages/probeStage.test.ts
• bun run --cwd packages/producer typecheck
• pre-commit lint/format/fallow/typecheck

[miguel-heygen]

Consolidated with the related duration and timing correctness fixes in #2405, which preserves this PR’s behavior and regression coverage.