This is a very wide question with no one rule. Generally, the further back in time you go, the more you tend to find composer/performers who would play lots of music, including their own. Beethoven and Chopin were highly regarded as pianists ( and young Beethoven could even handle a viola) Schubert was perhaps as highly regarded for his ability to improvise and accompany singers as he was for his compositions. The 17th c. lutenist Kapsberger was also very highly regarded for his ability to improvise: which has made his written works something of a challenge for performers, as they seem to be simpler versions for what he actually did. Some performer-virtuosos wrote pieces to show off their own chops, like Paganinni and Rachmaninoff. But even in the more recent past, Leonard Bernstein could do almost every musical task amazingly well except ( according to Stephen Sondheim) sing, and Frank Zappa both composed and was a great guitarist.

But after composition became its own career, composers did not always have to be very proficient: Satie was famous for asking other musicians to play something he'd just written on piano, so he could hear it. And modern performers have to spend too much time, generally, maintaining their proficiency. Does any recording of John Cage playing Mozart exist? Would there ever have been any reason for him to make one?

With the advent of the modern recording studio techniques allowing the swapping of sections, editing of mistakes, and equalization and reinforcement of tone, though, you could say that recent recordings of pieces by, say, Chopin and Beethoven probably have been made more flawless than when originally performed. Whether they have lost something important in that process is a matter for debate.

You might also want to post this question in /r/classicalmusic, as there are a fair number of professional classical musicians and classical music historians who peruse that subreddit.

You asked if composers were "really good at playing their own music?"

A follow-up question from me would be: Is this an objective measure? And how would one assess the "goodness" of a music performer? And, is it even knowable, that is how can one assess the "goodness" of a performer from the past where there was no audio recording?

For instance, I've read that Bach was an extremely skilled and talented keyboardist (as well as a composer, obviously). But how do we know he was talented at performing, aside from what other's wrote back then? We have no audio. How do we know if his talent was on par or better than a top tier musician's today? Can we ever know for sure?