Studying kanji & vocab

I hope I’m able to write my question properly since English is not my first language.

I’ve studied N5 and most N4 kanji already on their own, but now, going further into N4 and some N3 kanji I’m beginning to wonder if I should also study the vocabulary that each kanji creates by adding hiragana, such as verbs, or another kanji alongside. For example, I was studying the kanji 世 and saw that l, if I add 中 before it, which is a kanji I’ve already studied, I can create the word 中世 which means the Middle Ages. This made me think of taking each new kanji and checking the vocabulary I can add with kanji I already know, and so study both at the same time: the new kanji and new vocabulary.

Is this how you study kanji/vocabulary? Would it be better to keep studying kanji on their own and later on study vocabulary?

Thanks!