"Watch What You Eat" badge

You need a Garmin Connect+ subscription for that badge. You can distinguish them from normal badges because Gonnect+ badges and challenges have plus (+) symbols around the image.

I have it, but I do not have the glance or widget on the watch to log a food. Maybe I simply do not know how to do it.

Garmin doesn’t currently allow food logging from the watch, not even through Connect IQ. There’s no food‑logging widget or glance because Garmin hasn’t built one, and Connect IQ apps aren’t allowed to add food logging. Right now, food logging for Connect+ is only available inside the Garmin Connect app on your phone.

So, this badge is not really achievable right now, isn't it?

Use the Connect app on your phone.

At least on Enduro 3 you can add the Nutrion glance and then log your food that way and get the badge. I have to add foods to my Nutrition Favorites list in Garmin Connect. After that I can select them in the Nutrition glance.