To be frustrated that DD is struggling to find a job in her desired field while her friends on skilled worker visas aren’t

So if all the well-qualified British philosophy grads were kicked out of the foreign countries they've settled in and came to give your daughter some homegrown competition for jobs, would that be better?

Philosophy is a worldwide enterprise driven by exchange which is choked by borders. I have no doubt your daughter knows this.

Well did you even bother to see what jobs do qualify before leaping to the ‘foreigners stealing our jobs’ trope? Historians and social scientists are designated highly skilled, as are heritage officers, PR officers and arts officers - which presumably they’ll be classed as. So yes YABU - sounds like sour grapes.
Lots of grads would give their eye teeth to get into the CS btw….She may not like her current role, but there are plenty of options for sideways moves into something closer to what she’d prefer.

No worries at all, its a weird old world in philosophy! It will likely be what her friend specialised in. She may have focused on aesthetics and the philosophy of art. She may have been published on a subject and that impressed the institute. Philosophy breaks down into so many categories. I'd love to hear what your DDs focus was, that might help think of other routes into interesting careers. Unfortunately academia is also very hard to break into, so a PhD is not a guarantee of a job sadly.

They have a masters in the subject, im not sure what more qualifications you'd want for a skilled worker, can you clarify?
And people are directed to hire the best person for the job... are you saying thats not whats happened here? That both of these roles were designed in a way that non British people (also are we talking passport holders or what) wouldnt be considered for them if they applied? That in the first instance, a British person who was more qualified and knowledgeable about the country in question has been turned down because they arent from that country in favour of a lesson qualified person?
Im really not sure how your daughter not getting a job is leading you to believe there's something fishy going on with the other two jobs, surely you must realise that as her parent, who has never hired her for a job....you arent going to be the most subjective judge on how she interviews....

I have a degree and masters in philosophy. Unless your DD either has a specialist or something unique she can bring that sets her apart (her friends have got specialist knowledge in their culture that got them their roles) then she needs to do a PhD and commit to academia. No one does philosophy thinking there will be jobs at the end of it. Do it because its your calling, and make academia your job or accept that you are unlikely to 'work' in this field. You haven't said what role your DD works in the civil service, but if she comes from a moral or analytical philosophy side and enjoys tech, she could study AI and data ethics. Many companies are hiring for this specialist role and she could make a great career in it with her background.