In general, how familiar are users with submitting the form with the “Enter” key?

Many sites, even big ones, seems to follow the practice of hiding search field under the button and then showing a full-screen form on click.

enter image description here Click to see the form

enter image description here No search button though

What bothers me is how many users do actually know that form can be submitted with Enter key (because these sites don't provide other clues or buttons on how to submit the form)?

So either they are sure users will know to submit form with the enter or just follow the trend without thinking about it?

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