Fix frozen text caret blink while editing

[yvette-carlisle]

Summary

• fix Frozen text caret repaint so the caret keeps blinking while text editing is active
• reset caret blink phase when text, backspace, or IME preedit updates change the edit state
• avoid alternating caret visibility on successive input events by using per-edit blink timing instead of sampling a global phase

Verification

• cargo make test-rust
• cargo make lint-rust

Tracker

• XY-239

[yvette-carlisle]

@codex review

[chatgpt-codex-connector]

Codex Review: Didn't find any major issues. Chef's kiss.

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