There are a lot of things that I enjoy spending my time with, but it's easy to recognize my favorite ones because I can't barely see the time passing by when I'm engaged atin one of them.

"barely" is a negative adverb, it's about how something is so small that it almost doesn't exist. So "can't barely" is an ungrammatical double negation - you want to say that your capacity to see is so small that it almost doesn't exist, you "can barely see". Natives make this error very commonly.

"engaged in", "engaged by", "engaged with". "at" is not right here. Very difficult to explain why.

Enough with the miystery: iI love reading and playing videogames.

Probably a semicolon is more natural here.

While the books have keept me company since childhood, my love for videogames had the opportunity to grow just recently when I bought my very first gaming PC.

Simple present is okay, but the most natural tense here is present perfect. "an ongoing state or habitual action, particularly in saying for how long, or since when, something is the case".

Although I already considered myself as a gamer since I was a little girl, I never really had the time to play when I had to share the controller with my father and younger brother.

On the other hand, I don't like any activities that require a lot of people together: as a person who might be on the autistic spectrum, I'm very sensibltive to noises and get quickly overwhelmed by social interactions.

Again, maybe a semicolon would be better here.

"sensible" and "sensitive" are very easy to mix up. "sensible" is about making good decisions, it's "sense" in the meaning of wits, intelligence, correct judgment. "sensitive" is about the *act* of sensing, the senses, sight and hearing and touch and so on. Detecting things and reacting to them.