I've recently upgraded to Monterey, and while I normally use the Unicode HEX keyboard to input accented/special characters, it ignores characters whose codes start and end with "0", making it impossible to input "a with grave accent" (U+00E0), but "ᄐ" (U+1110) and "é" (U+00E9) work.
Seems like a bug, and is a big nuisance.
Update: Fixed as of MacOS 13.3!
I think all you can do about this is complain to Apple and use Character Viewer or the ABC Extended keyboard instead.
Making a custom layout for the characters you need most often with Ukelele may also make sense. Or creating text replacements for them (for example using the hex codes as the triggers).
Update: Still broken as of MacOS 12.6
Update: Still broken as of MacOS 13.2
Update: FIXED AS OF MACOS 13.3
I think 256 codepoints are affected, but not all are occupied. This chart shows them:
