To break it down a bit…
Nautical height does not refer to altitude. It is a term used at one time to refer to seal level. QNH does not mean nautical height it refers to atmospheric pressure measured above nautical height. I was just hunting the internet for a reference. I have an old nautical navigation manual on my bookshelf that refers to NH when measuring tide levels with a sounding lead. I can’t seem to find an web version. Not surprising, it was originally written in the early 1600s. (Not my copy. I wish!)