[2023] Are zombies limited in number on the map? Or do they constantly spawn next to you?

No they aren't limited, yes they spawn 'next' to you; But 'next' to you should be out of your visual line of sight.

No there is no mod for a map limit, But the game has respawn volumes that once emptied will stop spawning in zombies in the area after awhile- Which is similar to what you're asking for. IE, Once you've cleared the area around your base a few times, you'll generally stop seeing zombies in the area- You'll just get one or two every once in awhile unless you generate too much activity.