My feeling is that in the UK 'staff' is MUCH more common in all contexts, while 'personnel' is a bit more 'formal' and perhaps theoretical. You'd not talk about 'supermarket personnel' unless it was some sort of ingratiating management-speak.
Here are some of the 'personnel' sample sentences from the UK dictionaries:
There's a severe shortage of skilled personnel https://www.oxfordlearnersdictionaries.com/de...
a change of personnel on the management team https://www.macmillandictionary.com/dictionar...
The new director is likely to make major changes in personnel. https://dictionary.cambridge.org/dictionary/e...
There are considerably more sample sentences for staff (I haven't quoted all of them, but this just gives an indication of how many more staff sample sentences there are!):
It is a small hospital with a staff of just over a hundred.
The staff are not happy about the new arrangement.
The embassy employs around 50 people on its full-time staff.
She joined the staff in 1996.
Peter became a very valued member of staff.
There is a good relationship between staff and pupils at the school.
The staff are not very happy about the latest pay increase.
There are over a hundred staff in the company.
He is on (= a member of) the editorial staff of the magazine.
medical/nursing/teaching/coaching staff
The hospital staff cared for me so well.
There are 12 full-time researchers plus technicians and other support staff.
female staff members
(British English) part-time members of staff
to employ/recruit/hire/train staff
He joined the editorial staff in 2018.
We are suffering from an IT staff shortage.
The company has a good reputation for staff training.
We have a weekly staff meeting.
(especially British English) on the staff a reporter on the staff of ‘The Times’
