Is there a limit to have many layers you can have in a leaflet map?
There is no hard limit but performance could be affected by client processor speed, client internet connection speed and the capacity of your server to handle incoming requests. In general I try to keep mine below 10 user-selectable layers. Using well set up base maps instead of lots of overlays should help, also I try to use GeoJSON layers. Performance is great for simple lines or polygons and up to ~ 100 points + labels. Also, when your data changes you don't need to rebuild WMS tiles and it can reduce data transfers.
There is no limit, but from a practical perspective the more layers you have visible, the more the user experience will degrade.