Queens traded, you don't have to castle?

Hello lichess comunity, I'm a beginner and I want to improve in my chess strenght. I don't know to much of theory, so in this game I traded queens and after that I was looking at the stockfish analysis and when I castle it shows that I lose advantage.

So my question is: After the queens are traded, I don't have to castle because the kings are stronger in the center?

en.lichess.org/OX941wP5J8QY

btw I was playing white and I castle in move 10

Without the queens and with that closed center your king is strong on e2. You just need to make sure the diagonal a6-f1 is not gonna be a problem. Instead of castling the engine wants to play a4 to secure the bishop on c4 (b5 and Ba6 could be a problem if your king were on e2). However I don't think castling is so bad.

It all depends on your opponents pieces, if you leave your king in the center — can he attack you there? Rule of thumb when there are still rooks and minor pieces on the board it's a bit risky leaving the king in the center. In your game if you keep your king on e2 I can envision later Black annoying you with Ba6+, but will it be bad? — can't know for sure.

Btw, SF doesn't criticize your castling as it is. It just sees that on move 10 castling is not so vital and opts for developing — 10. b3 to get the dark-square bishop out (after moving a2-a4) as c1-h6 diagonal is blocked or 10. a4 to prevent b5 (black is gaining a bit of space) or simple 10. Nbd2.

I'd personally play 10. a4 because it's multipurpose.

thank you so much for your answers! Now I've learned more from my own game :)