fix: show stages for single-room competitions

[coder13]

Summary

• show schedule stage labels when a competition has multiple display locations, including multiple NatsHelper stages inside a single room
• reuse a shared helper for both the main schedule and personal schedule views
• add a regression test covering the single-room multi-stage case

Verification

• yarn test --runInBand
• yarn check:type
• yarn build

Closes #59

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