するようになる (among others)

Hello! Thanks to some helpful explanations from some of the people here and my own research, I've delved into trying to get a basic understanding of how よう is used in sentences. It was explained to me that 'するようになる' means 'to become to do'.

Now then...I've been having major trouble wrapping my head around exactly what that means.

To become ABLE to do makes perfect sense to me.
もっと練習するなら、料理できるようになる！(If you practice more, you'll become able to cook!)

But I still don't understand what 'become to do' means in an English sentence, could someone help me understand? よろしく！

もっと練習するなら、料理できるようになる is not incorrect, but もっと練習すれば/したら is more common. なら conditional is a bit special comparing to たら, ば or と, especially when used with verbs.

恋人ができれば、料理をするようになる
If she falls in love, she will cook.(lit. she will be in a state that she cooks)

道路が整備されれば、観光客が来るようになる。
If roads are built, tourists will increase.(lit. the place will be in a state that tourists comes)

You can think ～ようになる means "to become to be in a state".