Maybe try the "Summarize Within" Geoprocessing tool.
The Parameters in your case are:
Input Polygon:the "connectivity polygons" layer.
Input Summary Features: "Habitat Quality".
Summary Fields:the Shape_Area field or your area field in your "Habitat Quality".
Statistic:Sum.
It will give you the aggregate area of your "Habitats" in each "Connectivity" polygon.
While performing the step before, you have the option to group them by a field in your "Habitat Quality" layer and add group percentage.
If this grouping option does not fit your case, you can apply another step after you summarize, that is, calculate the percentage by an expression, because in your new resulting table, you will have your "connectivity polygons", with a new Field that shows summed area of Habitats within each Connectivity polygon (usually called 'Summarized area in SQUAREKILOMETERS' or something like that).
So the percentage is 100 * 'Summarized area in SQUAREKILOMETERS' / Shape_Area.