Advice on what to do with my 1 year old on my days off work (going back part time)

Following! As this is the same set up for me and my little boy.. I mean I will put him in a school nursery probably around 3?

I would say any local play group will be good for socialising them, check out if you have a local council children’s centre as they often run free weekly groups. Then just make sure you/family members are getting him outside in nature so parks, woods, beach (if applicable) etc as opposed to just the garden. There’s also quite a few places around now that offer messy play for babies/toddlers but they are usually chargeable.

I’m going back to work this week. Part time as well and my son will be with various family members too. On my days off I’m prioritising quality times together such as playing with his toys, showing him how toys work etc, reading books, singing, messy play at home is a great way to help him explore different textures. We will be doing walks to the park/library. Please don’t feel the pressure to have to have jam packed days on your days off. Simple jobs such as washing up/loading the washing machine/putting washing away are enjoyable for them too, my son loves to help with these. Good luck going back to work xx

I really don't think you should worry about this too much. They are still so young and the main thing they need is love and support. They will learn everything else one way or another x

You could get an annual pass somewhere, so like Zoo, Aquarium, local gardens, national trust etc.. these can be great for them to learn about the world and nature. As others have said, playgroups that are on your days off, churches often run free or very cheap ones. You could find activities to do online, read to them etc..
The main thing is not stressing about doing stuff though, they will learn from you/ your family members doing every day things! You'll probably be stressing about fitting in cleaning, tidying, making food etc.. so I'd prioritise one day for that (this is what I'm planning to do returning 3 days a week also). Get baby/ toddler involved where you can with this, it might take longer but they'll enjoy helping you and its good for their development.

I’m going back to work part time and my little one is going to family or a friend. Most nursery’s/childminders book up fast so hard to find one last minute

I really wouldn’t worry too much about that at this age. My now 3 year old never went to nursery as I have been able to stay home. They do really benefit from that extra time with family/parents.
I have always made sure they still spend time with other children of a similar age. We have a couple of friends with children the same age so he will have at least one play date a week. From about 18 months onwards with my first we would also go to a farm regular, or to the park and playgroups so he is still socialising with children.
He’s a very confident, he never has trouble making friends at soft play and hasn’t been behind with any developmental milestones. There is honestly, development wise and social wise no difference between him and his friends that do go to nursery a day or two a week. Xx

Honestly? You need to find better friends that won't make you feel like a bad mum for YOUR choices. That being said, I work 0-5 and I'll always defend the amazing job nurseries do to give little ones the best start in life, but we don't teach anything they could not learn at home with the people who love and know them best. Especially before they're 2, the only socializing they do is "tolerate" being around others, they learn everything they need from the way you behave with them.
If you're worried about offering experiences, follow tick tok or Instagram accounts that you like, blogs from stay at home mums, Pinterest, that sort of thing. And spend lots of time outside and around the community: garden centre, parks, local groups, going to the shops, the beach, library, woodland areas.