If I had that compost bin, and I realise it is probably not your compost bin OP.
I'd remove all the twiggy bits and using a shredder or secateurs, chop it into smaller pieces. I chop ALL my twiggy stuff into 2-4 inch lengths as I prune so it is always going in small in the first place. I'd use a pitch fork to get all the uncomposted stuff off the top. Then, at the bottom will be composted stuff, pitch fork or dig that out into trugs/a wheelbarrow to use.
then put all the uncomposted stuff back in making sure you mix it and chop it as you go.
With the composted stuff, I'd sieve it. Removing as many worms back into the bin, and anything left in the sieve, back into the pile.
going forward, chop everything as small as you have time or inclination to do. Never put in greens without browns [so add shredded paper, crumpled newspaper, torn up paper, cardboard torn up etc] and also add in anything else that will help to kick start things so coffee grounds, tea bags, comfrey, nettles [not the seeds], male wee - are all good activators. Then make sure you turn it as often as you have inclination to do by going back to the first step of pitching everything out and back in again.
Better still is to lift the whole contraption off the heap, move it next to the heap and pitch everything on the top into the new empty bin. At the bottom is the stuff to de-worm and sieve. But the one in the picture isn't the easiest to move. Perhaps with two of you.
Also consider that all the goodness and nutrition is soaking into soil you will never use, if you have a heap that is away from where you are growing stuff. My top tip is to move your compost bin to the place where you are going to actually need nutrition. Then when you move it about, your soil gets a top up of nutrients as you compost. Then you don't need to sieve, you just rake the soil over, pick out any bigger uncomposted bits, and let the worms make their own way into the bin. Compost where you next need it - situational composting. Much easier on the back.