I see you are ipset, but would urge caution with any complaint, and what you include in it.
It does sound like he was bullying and scary in his manner. Unfortunately some officials can be - jobs like that (police, security, even teaching sadly!) CAN attract people who get a kick out of wielding their authority. (As well as attracting lots of nice people too!) This is not ok, but is it actually unprofessional? How does one define what manner it is and is not ok to have in this situation?
Your dd of course didn't find this experience pleasant. But, in a way, it shouldn't be a pleasant experience. She was travelling on the wrong ticket (admittedly only to a tiny extent) and got caught. It is in the train companies' interests (and all of our interests actually) to put people off doing that. Though it should be proportionate - we don't want a minor in this instance to feel abused and terrified.....
Can I ask exactly what happened with her phone? Did he really spend ages scrolling through her apps? Or just ask to see something that would prove her age, and she suggested the Vinted app, and he looked at that? That probably is reasonable in fairness. I can see that he did need to verify her age.
The crop tops issue has been discussed upthread - they are in the public domain, so no point worrying that he has seen them. She has put them somewhere they can be deliberately searched for by pervs the world over if those pervs so fancy - she may want to rethink that if she regrets the choice now.
As for phoning you - this is a 15 year old girl, old enough to travel alone and sell her own crop tops on Vinted, not a tiny tot. I can see that he can't really be pausing every time he stops a 15 year old to allow them a conversation with someone they say is their mom......
I am not saying your daughter's experience was pleasant, OR that this man isn't a jobsworth bully. Just that there may be reasons for some of what he did, so I would think through any complaint you make before you make it, and be careful to identify the things he did that you truly believe are unprofessional/against policy, rather than just things your daughter didn't like. It's not meant to be an experience she would like.
Of course I do hope she is ok. I understand your upset and would be just the same if this happened to my daughter. I am just saying we can sometimes get carried away by our instinct to protect our kids......