It’s crazy that the “I’m feeling lucky” button still exists, I probably haven’t clicked it in 20 years (though I’ve been using DDG for like the last five).
On DDG those words with the exclamation point are called !bangs, and you can search them by adding !bang to the search query. If you only put "!bang" without a query it takes to the landing page.
For other operators you'll have to look at each search engine's help pages.