Update: fixed by Reset this PC
As Microsoft Support suggested, I did a Reset this PC (Settings → System → Recovery → Reset this PC → Remove everything → Cloud download) and then installed all updates. Since then the display works normally after restart and after sleep. No more green tint or blurry text, and no more need for the dummy plug.
The firmware and drivers after the reset are exactly the same versions as before (UEFI 175.327.235, Adreno 31.0.133.1, Surface TCON 161.17.0.34). So it wasn’t a hardware defect. It was something left in the previous Windows installation that survived driver reinstalls, rollbacks and display registry cleanup.
My guess at the cause: the System Hardware Update 200.0.51.0 was installed while the laptop was connected to an older-generation Surface Dock with external monitors. That probably left a corrupted display configuration that only a full reset cleared.
Tips if you try this:
Back up first. A system image to an external drive is easiest (Control Panel → Backup and Restore (Windows 7) → Create a system image).
Save your BitLocker recovery key from aka.ms/myrecoverykey before resetting.
Don’t restore the full system image afterwards, or you’ll probably bring the problem back. Copy only your files and reinstall apps.
Install future Surface firmware updates with the dock and external monitors disconnected.