I think you should put in a simple privacy statement that comes down to "Archivy won't make any external requests" if it's going to be as simple as that, and then stick to it like glue. If it's not that simple, be accurate to whatever room you'd like to leave yourself, and then stick to that.
Not having a statement like that leaves the future open for a future git pull to change the landscape. Technically the statement won't stop that, but it'll keep the project accountable.
FWIW it's way more important for this sort of thing because it's a stack you have to invest lots of time and notes into and buy into long term. Were I going to run a personal wiki, I'd be very interested in knowing I could likely use it for a long time.
May not be archivy directly. But for example if the web pages use static assets like google fonts, jquery, they will send external requests thus leaking the presence of the self hosted server. Or may be some javascript plugin that phones home.
I haven't looked into redacting a privacy statement, might be a good idea :)