First images from Euclid are in

I wish there was a standardized way to let folks who run a website such as this one know how much a casual passer-by viewer enjoys the byproduct of their work.

There is. It's called dwell-time

You might be staying there a long time because you're fuming, so: nope.

If you're in the EU (particularly Germany, France and Italy, who are the three largest funders), you can let your representatives know you appreciate ESA's work.

You used to be able to sign a guestbook

You are of course right that there are lots of potential motivations for spending extra time on the page. But it will likely be interpreted as enjoyment in the absence of other feedback mechanisms.

Esa has social media accounts, pretty sure some intern will see if you ping them, I don't imagine they get much traffic