No BufWritePre when using ZZ

Hi all:

I keep a timestamped backup copy of any modified file whenever I do a
":w". For this, my .vimrc includes the following lines:

" backup settings
set backup " keep a backup file
set backupdir=~/Backup/vim,.,/tmp
" next line prevents overwriting old backup see also :help bex
au BufWritePre * let &bex = '~' . strftime("%Y%m%d_%H%M%S%Z")

Interestingly, BufWritePre works with ":w", however, does not work with
"ZZ".

Does anybody know why this is the case? How can I make it work with
"ZZ", too?

Thanks for any hint.

Best,
Claus

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