There is no clear answer to this question.
Firstly it depends on the care plan – because if it’s in there, it must be funded.
Secondly, self employed PAs would decide what to invoice for and it would be part of their fee, and their own expenses deduction from their income.
Employed PAs are either volunteering their vehicle, or asking to be reimbursed for travel, like any other employee would.
If the payment from the council doesn’t cover the cost of the service including those expenses, one would be able to contend that the package was not sufficient, but very few people understand that they need to do that.
Expenses whilst out supporting someone might be regarded as part and parcel of the cost of meeting the need if for instance there was an eligible need in relation to social inclusion and accessing facilities in the community, or the cost of a meal might be regarded as something that an employee pays for in any event during their working day, whilst the extra cost that is not their choice might be regarded as disability related expenditure (DRE) (and allowed as a deduction from means, thus reducing one’s charges for care), because not every outing is ‘needed’ – some will be said just to be ‘wanted’ and there has to be some compromise somewhere.
The amount allowed to anyone for the meeting of their needs, (and DRE amounts allowed as a disregard from charges) are just like any other decision made by a council – subject to public law challenge for irrationality, unfairness, breach of human rights, or illegality.
It all comes down to how clued up one was at the time of negotiating one’s care plan, and how specific one obliged the council to be at that time regarding inputs and clarity, not just outcomes. If one missed that chance, one should ask for a review.

My care plan has always stated I am unable to access the community, activities, appointments etc without transport, aids and carers. The box is always ticked that transport will not be provided or included in budget. My carer who had a car was expected to take me out on my social time, so my food shopping, pick up my prescriptions and take me to all hospital (despite which hospital) and doctors appointments with there car and there fuel. I have lost that carer now after 6 years especially due to displacement from no fault section 21 causing me to move further away & recently a fire losing my home & all possessions with no insurance & single mother. Now she has left my carer has no car. Since December I have not been able to leave the house, attend appointments, take my child anywhere, take her to appointments or school, missed hospital appointments, not been seen by a GP since before the fire. Not been able to even pick up milk when I’m alone & ran out or cat food, or prescription when one of them wasn’t ready the same day as others. Me and my daughter have been left isolated. No family, friends, no social time, housebound effecting both of our mental heath causing my mobility and muscle loss to worsen. I have a son who lives alone has now registered as a disability as having seizures very very frequently & struggling with mental health. While I am in this horrendous situation with no possessions pushing me to bankruptcy I have had to get Ubers to and from my home to his to check on his at least twice a week and calling emergency services costing me approximately £50/70 a week. How is this supposed to be acceptable? I need urgent assistance/clarity