I think you need to:

1. merge all your layers using "Merge Vector Layers."
2. Prepare your points that you want to get statistics .
3. Run spatial join with "Join by attribute location (summary)" (Use count as summarize field.)
4. Number of layers in specific points will be shown in the attribute table of the output

I think you need to:

1. Merge all your layers using "Merge Vector Layers."
2. Prepare your points that you want to get statistics .
3. Run spatial join with "Join by attribute location (summary)" (Use count as summarize field.)
4. Number of layers in specific points will be shown in the attribute table of the output