Ok so if you're gonna do this again, ideally you should practice drilling into a piece of scrap wood. If the drill bit broke going into wood, it means your control of the drill really needs practice and you put pressure on the bit in the wrong direction. Try to think about pushing the bit into the hole you're making in a *perfectly* straight line, making sure not to bend the bit, not to put any pressure on the bit that isn't directly along the axis of the hole.

There's a challenge to this, because your hand isn't directly behind the bit when you hold the drill, so if you push your hand directly towards the wall without compensating, you will break the bit. You can see how this happens if you take the drill, and without pulling the trigger, just push the drill against a surface with a limp wrist. You'll immediately see the drill change angle. That angle change breaks bits. You need to compensate for that tendency or you'll keep breaking bits.

This difficulty is very normal for someone who hasn't done a lot of drilling. Breaking small bits is a rite of passage tbh.