The word 'discreetness' is correct and usable in written English.
It is a noun form of the adjective 'discreet,' which means showing good judgment and being careful in one's actions and speech. You can use 'discreetness' to describe the quality of being discreet, or the state of being discreet. For example: - The politician's discreetness helped him avoid any controversy during his campaign. - Her discreetness in handling the sensitive information impressed her boss. - The hotel prides itself on the discreetness of its staff, ensuring guests' privacy at all times. - The thief was caught due to the lack of discreetness in his actions. - The mother reminded her children to use discreetness when discussing family matters in public.
Dictionary
discreetness
noun
The state or quality of being discreet.
Exact(3)
This discreetness results in part from a fear of class hatred and a lingering conviction that what happened in 1917 could happen again.
It is a curious fact that, while "continuity" and "discreteness" are antonyms, "continence" and "discreetness" are synonyms.
Discreetness speaks to integrity.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com