The Flex Keyboard's backlight is basically hardwired by Microsoft to come on whenever it detects any input — that's just how they've designed the firmware. Unlike a Surface Laptop where the keyboard is built into the device and holds your backlight preference, the Flex Keyboard treats "backlight on" as its default resting state. The recent firmware update likely reset or reinforced this behaviour, which is why it's now lighting up on wake from sleep even though you had it turned off before.
Press Fn + F5 to cycle the backlight off after the device wakes. It's annoying but currently the most reliable workaround.
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Since the issue appeared after the firmware update, try resetting the keyboard:
Detach the keyboard from the Surface.
Hold the Esc key for about 5 seconds until the LED on the Fn key lights up.
Reattach the keyboard to the Surface.
Check if the backlight behaviour changes.
Open the Surface app → select your Flex Keyboard from the bottom menu → tap Firmware update.