Learn Dutch: Het ouderschap is uitputtend, nu we zo weinig slapen. - Parenthood is exhausting, now that we sleep so little.

Because it is in a subordinate clause. The word nu (now) is acting as a subordinating conjunction here, meaning "now that". This type of conjunction kicks the working verb to the end of its clause. That's why it is nu we zo weinig slapen instead of the normal main-clause word order (we slapen zo weinig).

Can I say nu dat instead of just nu to mean "now that"?

You don't need to! While you might occasionally hear native speakers say nu dat in casual speech, simply using nu on its own is the standard, most natural way to say "now that" to introduce a circumstance in Dutch.

Is the -schap in ouderschap similar to an English suffix?

Yes, it is very similar to the English suffixes "-hood" and "-ship". It turns the noun ouder (parent) into the abstract concept ouderschap (parenthood). A helpful grammar tip: almost all abstract nouns ending in -schap are het words.

How is the word uitputtend (exhausting) formed?

It comes from the verb uitputten (to exhaust / to deplete). By adding a -d to the full verb, you create the present participle (uitputtend), which functions exactly like an "-ing" adjective in English.