Hello - I saw your other thread (your link above doesn't work for me though), hope you are getting good medical help now.
Agree with treading carefully given possibility of allergies. I would say the safest (and most nutritious) thing to add next is meat and/or fish. I'd stay off dairy for a while in your shoes, and probably be cautious with gluten too.
Fish is great as it can be cooked quickly (microwave works well) then mashed up with milk and added to any veg puree. And it's so healthy. Meat is a bit more of a pain, ideally to get it smooth you need to slow cook it in some kind of liquid (especially if red meat) and then puree it. Chicken breast is easiest, least fibrous. You could make casseroles and then puree them, that's what I did to make a "complete meal" in a puree iyswim.
You could very gradually start making food lumpier, first puree it a bit less, then switch to mashing instead of pureeing (though meat would still need to be whizzed as doesn't mash). You could try very soft risotto made with veg and stock for a more lumpy meal. Mini pasta (like orzo) or cous cous works too to introduce texture into puree/mashed veg meals.
Other finger food ideas - well cooked carrot, rice cakes, oatcakes, bits of chicken breast. Chicken and apple balls are a hit in my house.
You really don't need to go too quickly though, he's only 7 months, many babies are still only having a few spoonfuls of food here and there at that age, or refusing food altogether. You can be "baby led" in the sense of trying various things and seeing what he likes (and keeps down...)