Thank you Chris, your advice always is really good

Would takes a verb object. Here "we would " is an elliptical version of "we would spend." The statement is an implicit type 2 conditional. (rephrase) "Sunscreen emboldens us to spend more time in the sun than we WOULD SPEND otherwise (= if we didn't use/have sunscreen). Here, the modal could can replace would with no significant change in meaning. Like would, could takes a verb object. (rephrase) "Sunscreen emboldens us to spend more time in the sun than we COULD SPEND otherwise (= if we didn't use/have sunscreen).

Thank you Kyler Shea, very good answer, it's clear!

"Would" is a verb. It doesn't need a complimentary verb. It works alone. You can change "would" for "could" but the meaning is a little different. Also, switching "otherwise" and "would" sounds more natural. You can say: "Sunscreen emboldens us to spend longer in the Sun than we otherwise would" "Sunscreen emboldens us to spend longer in the Sun than we otherwise could" Both are good sentences