Make getNewScreenTimeToDisplay race-free by moving it to the native store/pull model

Background

#6722 fixes the fatal JavaCallback was already settled crash from getNewScreenTimeToDisplay under rapid navigation on Android (#6709). That fix makes losing the race survivable (crash → dropped measurement) but does not close the race window itself.

Why the window is intrinsic to the current design

RNSentryTimeToDisplay.getTimeToDisplay schedules a deferred Choreographer frame callback that resolves a live Promise after the frame renders. The producer (native frame callback) and consumer (JS promise / backing JavaCallback) have independent lifetimes:

• Native gets no teardown signal when a navigation is superseded, so it can't cancel the pending frame callback.
• com.facebook.react.bridge.Promise exposes no validity query, and even a check would be TOCTOU.
• The deferred settle is the measurement (time to first frame after navigation), so we can't resolve early to dodge the race.

The only atomic option at that layer is attempt-and-catch — which is what #6722 does.

Proposed race-free design

Move getNewScreenTimeToDisplay to the store/pull model that the other TTID paths already use: the frame callback writes the timestamp into the native screenIdToRenderDuration map (via putTimeToDisplayFor), and JS pops it later via popTimeToDisplayFor — same pattern as ttid-, ttfd-, and ttid-navigation- (see timeToDisplayIntegration.ts). A stored value has no long-lived bridge callback, so there is no "already settled" failure mode at all.

Scope / considerations

• Bridge spec change (NativeRNSentry.ts) → breaking, needs a @deprecated migration path.
• Must be implemented on both platforms (Android + iOS — the iOS variant of the settle-after-teardown risk was deferred in #6722).
• Changes the fallback contract in sentryeventemitterfallback.ts, which currently races the native promise against requestAnimationFrame; a pull model changes that timing and needs care.

Acceptance criteria

• getNewScreenTimeToDisplay's deferred measurement no longer relies on resolving a long-lived promise from a frame callback.
• No behavioral regression in TTID measurements on either architecture (New + Old) or platform (iOS + Android).
• Deprecation path for the bridge API change.