Google PageSpeed Insights can now tell you how fast your whole site is as a whole because it now lets you see the aggregated page speed data across your whole domain name. All you need to do is either (a) search using the syntax origin:https://www.domain.com, so for example origin:https://www.rustybrick.com or (b) do a query for any URL and in that interface, Google provides a link to see the site wide data.
Here is that link I was explaining in section B:

Notice how Google doesn’t have a PageSpeed score for my home page. But when I do the origin, I get a score for the whole site:

Here is for this site:

Here is for the home page:

This tip came from Dan Nutter on Twitter and it is pretty neat to see the site as an aggregate!
Forum discussion Twitter.

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