Learn Hardcore Indonesian: Pakaian kerjanya terlalu formal untuk rapat keluarga. - His/Her work clothes are too formal for the family meeting.

It usually refers to what you typically wear for your job (officewear, uniform, business clothes, etc.), not clothes that you physically work on (like laundry).
It’s a bit more neutral/formal than baju kerja.
- Pakaian kerja = more general, can sound a bit more formal or written.
- Baju kerja = everyday, casual speech.

In this sentence, pakaian kerjanya is best understood as his/her work clothes or their work outfit.

What does the suffix -nya in pakaian kerjanya mean? Is it his/her, or the?

The suffix -nya is very flexible in Indonesian. In pakaian kerjanya, it most naturally means his/her/their (third-person possessive). So:

pakaian kerja = work clothes (in general)
pakaian kerjanya = his/her/their work clothes

However, -nya can also act like a definite marker, similar to the in English, when the context is clear. So depending on context, pakaian kerjanya could also be understood as the work clothes (we’re talking about).

In a neutral, context-free translation, people usually read it as his/her work clothes.