well that's interesting
it appears to be a vent cored through the wall, not poked through the eaves
which is good
though I can't see the flaps being pushed open by airflow (looking again I think it is a plain grille, which is OK). Was the wind blowing towards that wall?
I'm sorry you've spent so much money with so little to show for it.
Both your installers seem to have done a half-arsed job.
Some pics of the vent hose in the loft will help a lot.
The flow with your existing fan may be weak, just run it continuously for now. If you can get a joss-stick, or a smoker, you can watch to see if the fan sucks the smoke.
It's possible to get a better wall-vent, and it may be that your hose route can be improved, but the main thing will probably be to get a more powerful fan.
This is a very good one, and quiet. For best noise suppresion, it can be mounted on a piece of thick ply, covered both sides with synthetic carpet, rubber underlay, or other sound-deadening material, screwed to the loft timbers. This means it will not annoy anyone if it runs during the night. My hearing is poor; I can just hear them if I am in the bathroom, but not if the door has been closed and I am standing outside. Pretty sure your hose and vent will be 4-inch/100mm, and you will need the Timer model. The example I show is suitable for a bathroom with steamy shower, and more than twice the power of your old one. If the hole in your wall is bigger, you can have a bigger duct and fan, and more power.
Same principles as the one shown before by
@bhm1712
i have been rather disappointed by Manrose quality and noise in the past.
68 litres per second (Manrose) is 245 cu.metres per hour
and Soler & Palau is 250m3/hr so quite similar.
Your existing fan probably has a nominal air throughput around 80-100 cubic metres per hour, the ducted fans can be two or three times as much, and, being more powerful, can blow air even against moderate winds.
Water droplets on the fan suggest it is cold, possibly cold air is blowing in if there is no non-return flap (easily added) though it would normally warm up with a minute of so once warm air is passing through it. The duct ought to be covered in your insulation so it does not get condensation inside (this is a real problem with flexible hoses, though a rigid duct can be positioned to run downwards towards the wall vent).