This is a picture of the extractor exhaust. I thought it was meant to go down in to soffit?
It does seem to be doing that though, seems to just go along to the end of the roof.
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Having had a bit of a battle myself with new bathroom ventilation, you need to do some research and decide on a proper way of venting the bathroom.
Sometimes the above is done and people come and go and there is enough through draught for things to work themselves out.
However, like you find out, sometimes not.
These things aren't easy as i discovered.
My 2c based on my experience:
You could go to the soffit. This is a bodge though. Currents can pull the damp air back into the roof space via the same soffit vents. This seems to be a common problem.
You also have the issue if drips, etc, frost, on the soffit, roof, pavement and mould, damp, discoloration etc blah blah.
The very best way to vent is through a roof tile vent. There are no downsides to this for the roof, however, as you may yet to find out (but will) with your current set up, condensation is a bugger. In a poorly insulated attic like yours, you may not see much of it but you have to get rid of it regardless.
I can't tell by your picture but it looks to me as if your flexible ducting is deadleging. That is, it doesn't flow one way or the other. Also its corrogated. It will be full of water. This may be rolling back into the vent or ponding up to get to the soffit but either way, your setup is everything wrong.
If you do make it out of the roof space, you then have to consider back draught. Without backflow prevention, you are going to have a cold and draughty bathroom
If you are happy with the soffit route, you have to come vertical off the vent and then using solid duct, run in a slope as low as possible to the soffit. Fitting a backflow preventer on the outlet.
Not ideal, but will solve most of your issues.
Ideally, you should come out of roof via a tile and as near vertical as you can to the bathroom vent.
Don't use Flexi hose and if you do, keep it taught.
Don't put the fan on the same structure as the ceiling as it promotes noise.
Put a condensate drain as low as possible in the vertical ducting and route the condensation outside. (Drain pipe works).
You can insulate the duct to stop condensation somewhat but drain is far better.
If you Google "condensation drain vent bathroom" you'll go down a rabbit hole of info.
I learned the above by experience.
Whilst you are at it, update your attic. Property insulation on the joists. A good attic hatch, insulated. And clean up the eaves etc.
If you unclog the eaves without insulating properly, you'll be burning the gas.
The above is just my opinion. Best o luck.