Fix Local Studio session fidelity and streaming performance

[0xSero]

Summary

• preserve legacy Local Studio tool lifecycle events and always render tool activity
• serialize rapid follow-up turns without loss, duplication, or settings drift
• batch streaming updates at display cadence and prepare iOS/Android 2.0.0 build 200000260

Validation

• cargo test -p codex-mobile-client --lib (798 passed, 7 ignored)
• cargo test -p codex-slingshot (14 passed)
• live Pop!_OS Local Studio command + rapid second-message acceptance
• signed iOS device and simulator builds
• Xcode test scheme (223 passed, 1 skipped, 0 failed)
• Android emulator build and :app:testDebugUnitTest

[0xSero]

Closing as superseded by #319 (merged as 0824605d), which fixes the same stalls at the Rust store boundary rather than at display cadence. This branch has been conflicting against main for some time and carries stale release metadata. If any specific UI change here is still wanted, please re-cut it against post-#319 main.