Diary entry - Recently, I've been learning baking.

[emsr2d2]

How about “I like sleeping/I like to sleep”? Which is better?
Should I use “like” as the in the same way of using as “learn”?

They're both correct and neither is "better" than the other as standalone sentences. I'm not sure what you mean by your second question. "Learn" is more commonly used in the continuous or in past tense. We wouldn't, for example, say "I learn to play tennis". We'd say "I'm learning to play tennis" if it's an ongoing current situation, or "I was learning/I've been learning/I learnt/I have learnt/I had learnt to play tennis" for various past time contexts.

 

[Tarheel]

Probably more natural is this. (See below.)

I enjoy a good nap from time to time.

(Yes, I know that's probably a bit off-topic.)

 

[Tdol]

In British English, I like to is often used for restricted rather than general conditions: I like to sleep in front of the TV after dinner. This is different from always sleeping when the TV is on.