Korean IME broken again after update to 2.1.235 (regression of #35307)

Following up on #35307, #25186, #22732 — this regressed again after updating to 2.1.235 (released 2026-08-18).

Environment: Windows 11, Windows Terminal, Microsoft Korean IME, SSH into a remote Linux host, session inside tmux.

Regression timing: Worked fine on the previous version. Broke immediately after auto-update to 2.1.235 installed (2026-08-19, ~08:44 local).

New data point — workaround found: Korean IME composition fails in Claude Code's input line, but if another Win32 app with a normal visible text caret (e.g. Notepad) is open and visible on screen, Korean input starts working in Claude Code. Minimizing that app breaks it again immediately.

This is consistent with the "fake cursor" root cause described in #35307 — Claude Code doesn't move the real console caret, so Korean IME can't anchor its composition window. When another app is holding a live caret, Windows seems to fall back to using that caret's last known position for IME, which "accidentally" makes composition work — until that caret disappears (app minimized).

Might help narrow down the regression since it points at a specific version (2.1.235) and a reliable repro/workaround.