Easier said than done, I would have thought, to get a part time job. ( Also the lister might not want one). Anyway, my advice is don't rush into doing anything straight away, get a feel for being retired first, and don't let people make you feel guilty for being retired!! Everyone is different. Some people will find the adjustment hard, others won't.
Think about things that interest you (not everything will involve a huge financial outlay, in fact most things won't), have you got hobbies that you will be able to spend more time on, for example. (Gardening, a sport, photography, bird watching, etc).
After a rest, you might indeed want to volunteer, but keep it on your terms or it may turn into an unpaid job with the expectation that you will turn up on specific days when in fact you might just want to stay in that day and do very little!
There are plenty of short term courses on futurelearn which are free (unless you decide you would like a certificate upon completion which you'd have to pay for) and they cover every category imaginable. I've done lots and enjoyed them. It keeps the brain cells active ?.
My main message though, is don't panic. Relax and enjoy this new stage in your life.