Here’s the randomness of my thoughts.
I’d start with removing the fake grass and planting there first since you desire turf. You might find you can raise the bricks at the edges to slowly enlarge that area yourself making the project much less expensive. It would also let you know what kind of soil you will be dealing with, give time to consider uses for the bricks if you want to reuse, garden plans for the future. I can guarantee that turf will be a lot more work than cleaning the pavers if maintenance is your main concern.
I would also live with the brick patio and see how I use the area. If you barbecue and eat outside a lot having a solid surface is really nice. We enlarged our paver area to avoid muddy areas where turf just wasn’t practical because of heavy use. Depending on the micro environment of the space you will also learn if you will want a shade structure. We ended up putting a cover over our barbecue area for protection from rain as well as sun And included a fire pit.