I wouldn't add a ceiling light to the kitchen, but definitely add more recessed lights. Switch the groupings separately depending on use. Add dimmers to all switches.

You could do a chandelier/pendant over the kitchen table.

Architectural level residential recessed lights are available from Element, Lucifer, DMF, and USAI. For task lighting,1500 lumens at the fixture is what I'd look at in a 4" trim. 450 lumens is the minimum recommended at the counter surface . Lights are positioned 6" in from the counter edge in pairs to avoid shadowing your work. Aisle lighting can use flood led bulbs. Task will require spot or wide spot led bulbs. 3500K color is commonly used.

do you have a mock up of what the kitchen will be? the pitch of ceiling is high but the kitchen 11 x 11 is smallish. if you can show where and how high the wall cabs will be etc. I might stick w sconces and under cab task lighting. Where the room opens up you can do other things .

directional sconces shown ... but cant tell where /how many because there's no plan shown. you can mount these atop upper cab molding in addition to above window spaces.....and keep the lighting cascading right down onto your use areas instead of so high at 15 feet. in the eve you can use the under cab lights to illuminate a few areas .

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Here’s a couple pictures of the design. I will also add under cabinet strip lights.

An exhaust hood is preferred over the range. All drawer base cabinets. You'll need lighting for the sink.

An exhaust hood is not in our budget. We use the microwave every day and, we are limited in storage. We would lose storage space. We are in South Florida. Labor is crazy expensive. I already have lighting planned over the sink. My question is whether or not I should add a light in the center of the kitchen space. Maybe just a recess light or a chandelier.

A vaulted ceiling with an angled wall presents a challenge for simple lighting.

You cannot rely on the sink's overhead wall mounted light or undercabinet lighting to provide task light inside all the upper, base, and pantry cabinets.

Though a central chandelier might solve for that, it would probably detract from the space and conflict with the sink light and future dining table chandelier. Note you do not need to light up the open floor space within the Kitchen.

So it appears that your idea of gimbal recessed lights is right on. Placement would be based on a plan layout of the cabinets. Because of the vault and angle wall, they are not going to match perfectly with the cabinet layout, but will meet their purpose of task lighting. I would initially think choosing 6" fixtures would be better for the 10'-12' height and amount to less fixtures punched in the ceiling.

FWIW a sconce defines a wall mounted light at human height, not overhead.

The kitchen table in the picture will be gone. We will have a smaller round table (40-42") which will be in front of the patio door, slighltly to the left. We have sofas in the family room next to the kitchen space. There's also a celing fan in the family room which will be updated.

Would a pendant above the kitchen table look too crowded? kitchen picture before demo.