Answer by she_weeds for Getting list of intersecting layers into a field in a polygon table

You can try this in Field Calculator:

array_to_string(    array_foreach(        array_filter(array_remove_all(@layers, @layer),                     overlay_intersects(@element)),                 layer_property(@element,'name')),', ')

Explanation:

1. Get a list of layers using @layers
2. Take out the current layer from that list using array_remove_all(@layers,@layer)
3. Filter that list with array_filter() using condition overlay_intersects() to test if any feature on each layer intersects with your current layer.
4. Iterate through the resulting list with array_foreach() and extract the name for each layer with layer_property().
5. Finally, convert the list (array) to text (string) using array_to_string() and your preferred delimiter.

Example (shown in label of polygon layer 'temp' - other layers include point layers but principle is the same):