I personally had one or two issues with the video you used. I’m not sure they were being literal when they said は means “as for”. は doesn’t have any meaning, it has a function. Translating it this way can help people understand how は works within the sentence, but I’ve also seen it confuse people too. I once saw a post from someone who said 私は難しい incorrectly thinking it meant “It’s difficult for me.”
Some of the things you mentioned also weren’t accurate.
a) Generally speaking, cats are liked [猫が好きだ] b) As for me, cats are liked (-> I like cats) [私は猫が好きだ]
Sentence B is correct. Sentence A however is just sentence B with the subject/topic omitted. You’ll have to infer the it from the context, but it will be “I” in most cases. I don’t think there will be any context in which it will be understood as cats being generally liked by everyone.
a) Generally speaking, as for cats, everything about cats is liked. [猫は好きだ] c) As for me, as for cats, everything about cats is liked. (-> I like cats) [私は猫は好きだ]
There are a few issues here that are a little misleading. は好き can be used like this, but in my experience of looking at sentence from native Japanese speakers, it’s mostly only used in the following three ways:
Comparisons, for example 私は猫は好きですが、犬は好きではありません (I like cats, but I don’t like dogs.)
Together with a conjunction like ですが、ですけど、でも, for example 私は猫は好きですが、飼ったことはありません (I do like cats, but I’ve never had one.)
Together with になる, for example 私は猫は好きになれませんでした (I wasn’t able to become a cat lover.)
Number 2 and 3 can be replaced with が, but は is preferred for number 1.
私は猫が好き also doesn’t quite mean you like everything about cats. It’s the same as saying you like cats in English, you’re making a general statement without specificially identifying what you like about them. I like everything about cats is closer to 猫の事が好きです or 猫の全てが好きです.