I study my 5 min and longer games. There's an open source chess game database where I input the games. I set it up so it runs stockfish and I can write annotations and notes.

I will go over each game and write notes on what I was thinking, potential things I could have done better, mistakes I made, tactics I missed, mistakes my opponents made, etc. That type of thing

Then after going through and writing a sort of summary of the game with a couple takeaway points I turn on the engine and go through a second time to see if my analysis was correct and see things I missed. One thing I learned very quickly that the engine makes you look like a dumbass 😅

Although from what I've read even people like Carlsen experience that.

Saving all my games in the database is useful because I can see my win rate in specific openings. So for example I'll play an opening like let's say French defense on White's side. I play the Tarrasch variation.

1. e4 e6
2. d4 d5
3. Nd2

Here the typical response, and one I have a good win rate against, is 3 ... Nf6 which leads to the mainline. However, through looking at the opening statistics I saw I had a 30% win rate against 3 ... c5 (terrible compared to the 65% win rate against 3 ... Nf6)

So seeing this, I do some research on that specific line of the opening and I now have a response. Through this type of trial and error after game analysis you start to learn many sidelines of openings and you better understand the ideas and themes prevelant in those types of positions.

In addition to all that, I study openings using books. I play the same openings every opportunity I can. I always start with e4 and for example I have a response against the three most common moves.

1. e4 e5

Here I play the Danish Gambit

2. d4 exd4
3. c3 dxc3
4. Bc4 cxb2
5. Bxb2

I have read a book about this opening, as well as studied it through engine and of course the post game statistics.

Against the Sicilian I have the Smith Morra (excellent book out there called "Mayhem in the Morra" I highly recommend)

1. e4 c5
2. d4 cxd4
3. c3 dxc3
4. Nxf3

And of course against the French I have the Tarrasch Variation which I outlined earlier in this comment. I try to stick to the same openings every game and I try to learn more about those openings. This way over time I've picked up many many sidelines of openings and I know the best move to strange or unusual sidelines.

So... to finally answer your question.

It's both. I study and I play. At the end of the day, you need to play otherwise you will never improve. However, you also cannot just play. You can play mindlessly for years and you will never get any better.

There are people online with tens of thousands of bullet games and they are rated 1000 still.

You need to study and analyze your games, as well as outside material, in order to be able to take that practice and internalize the lessons.