I thought to upload some more photos so its clearer:

The image below shows where the square drain is. The concrete slants to that.

This image shows the slant, its about 10cm lower to the left.

Where the concrete meets there is no gap. See below photo. Would it be better if there was one?

I drew over the photos to make it show the board direction that you suggested. Is this what you mean by across under the pergola and down where the spa is? I also added in the spa, umbrella and enclosed raised step that is around the spa.

I also indicated the rectangular spaces on the side part. That is to have a few boards shorter to create a some holes and then plant a lilly pilly to hide the fence. Would this be better with drainage?

If it was flowing in before then it will again. The battens should lie in the direction of drainage flow. Make sure water can freely drain from under the deck.

if your rough mark ups are direction of the boards over the battens running perpendicular then yes that's how you'd do it....battens should be approx 20-30mm min thick so decking sitting off concrete if that makes sense - as Kate said it's about water being able to freely drain from under the deck... . looks like you have a decent pit drain for surface water in the lawn which is good to see...I misinterpreted your original post re the gap - you were referring to the garden bed next to the fence - i thought you meant between the concrete and 90mm....if the water from the undercover slab can get out and onto the outside/spa slab that should be OK but it will be in the detail of where these two slabs meet and managing batten positions/directions - try make sure to setback the first outside batten, (but decking would have to cantilver a bit so not ideal so there's a little channel for the water to run off from the covered concrete otherwise it will be boxed in....alternatively you could put a plastic strip drain between the two sections and cut out in the sides in each section of the batten spacing to the under cover area and so the grate/grill separates the two sections of decking - not ideal aethetically but addresses the drainage issue......Another option to consider is to change material / pave the under cover area so that water can run off from a higher level onto the external deck level then drain via the external sloped slab

should there be an expansion gap between the old and new slab, I think that paving the whole area could be a simple option, what is the step down to the current slab from the house?

it's a tricky to resolve elegantly whenever you try and get water to make right angle turns. Ideally everything falls out to the back fence and then pick it up in a drain there then no step or change of direction... another idea is to pack up the battens on decent spacers and run it all the one way so the water can run more freely under the battens but not that ideal either and you're governed by the window/door sill heights and the concrete level so it's tight.....assuming it's just a 100mm paving slab could pretty easily get it cut back to fit a strip drain between the two slabs if decking finish is really what's wanted. you could then batten out over the top of the drain and then start the different deck/batten direction running to the grass on the outside of the drain but having water potentially getting trapped under deck on relatively shallow battens not ideal as weather events are getting more severe...

Also it looks like you are downhill from neighbouring property so having drainage for potentially run off is something to consider, on the high side and so if you cut a channel in you could also get a drain into that garden bed area and connect/divert any potential surface water pooling / trapped around to the main pit in the lawn....it may seem like more work now but you may be thankful sometime down the line in a deluge that you went to the effort to get it in place - easier to do now with a bit of concrete cutting and plumbing than down the line retrospectively