More pics of the area in daylight would be helpful, as would a drawing of the area to show how much space there is. A floor plan, but a patio floor plan! Also some idea of your budget and what do you do in the space besides dine..do your guests or family hang out when you're not dining?

Yes on moving the seating area for the fire table and make the patio all about dining! Have fun

Daylight pics and a to scale plan since hard to get a feel for the size of the actual patio . Can you enlarge the patio ? That would be my choice then you could ahve all the stuff you want . I am not a grass lover so for me a huge deck or patio is just plain more useable for outdoor entertaining.

Pergola.

Picture also from the patio level would help

You could add more plants or some garland with flowers ?

I will take some measurements and add photos.
Lots of kids in the neighborhood hang out at our house. We have a fire table but one day I’d like a fire pit with seating.
We cook a lot so a fun dining area is important.
I definitely want to expand the space out more though feel a bit limited with the tree though I won’t take it down because it provides awesome shade.

Based on just the one overhead photo you posted, it looks like the flow would be improved if you switched your dining table and chairs with your lounge furniture,