the ducts are probaly retained onto the ends of the fan with overcentre clips like you might find on an instrument case. Loosen those and the ducts should pull off. Have a look down them both to see if they are choked with fluff, birds nests, insulation fibre or anything. You can clean grills with a paintbrush and hoover hose. Look at the connection of hoses to grilles.
If you run the fan with the ducts removed, you should feel a strong air current going in one side and out the other. Presumably it has been fitted the right way round.
there will be a control to change the run-on time, usually they can be turned up to 20 minutes. You may as well set it to max. Some fans also have a 2 or 3 speed setting. Turn it to max.
I don't know where the controls are on yours. There should be a model type and number on it, and you can download the instructions from the maker, or ask their advice.
I agree that if the ducts are not obstructed, and you leave the fan running for 30 minutes with the door and window closed, it should remove all the steam. Opening the door or window will prevent it working efficiently. Turn it on before you turn on the taps.
It looks like the ceiling vent is next to a downlighter. This might be a problem. if the hole in the ceiling is not sealed, the grille might suck air from the loft instead of from the room.
the mineral wool insulation is very badly laid. It should be in large panels or rolls, not chopped up, completely covering the ceiling between the joists.
measure the distance between the joists and buy yourself (at least) one roll of mineral wool, of the same thickness as the depth of the joists so it lies flush. You can cut it with a breadknife or large wallpapering scissors. I recommend the type treated with Ecose, which does not shed irritant dust and fibres, and is dark brown and silky. It is made by Knauf but widely sold as an own brand, and "Ecose" will be clearly marked on the packaging. If the old insulation is chopped up, or is yellow fibreglass, pack it into bin bags and tape them up for disposal;. I find it very irritant.
you can wash fibres off your skin by showering with cold water.
wear a mask, gloves, a hat, and long sleeves.
you can loosen the fan body, and put a large piece of rubber carpet underlay under it before screwing it back down, this will reduce noise transmission. If you can get them, put rubber washers, such as tap washers, under the screw heads. It must be well fixed so it cannot vibrate.