You don't just push ducts into framing. If there is ductwork, you work around it.

Those wall vents don’t look like they are connected to ducts running through the soffit. They appear to be below the soffit elevation. Where is your HVAC located? Above or below? Try to figure out how/ where your ducting is located.

3-10K per soffit. Or undoable. Soffits full of electrical and HVAC probably have some plumbing venting in there too. Or structural beams.

Are you renovating your kitchen or just want to add lighting? To remove the soffit the cabinets will need to be removed and hopefully not damaged. If you do not take cabinets to the ceiling you get the bonus of extra dust collection on top. Whatever, please try to avoid putting “stuff” up there 🥴.

Make a plan after you know what's hiding inside. We ran plumbing from a bedroom inside a tray ceiling because of the slope that was needed...it was the only way to do it efficiently because the space below is open concept. Someone might one day assume that it's only a beam or duct work up there...

Thanks guys for all the info that really helped. Yes I do plan to remove those cabinets and install new ones to the ceiling. That’s the plan for removing the soffits. So I guess there’s no way to see what’s inside it without making a hole. Do u think we can just see through the top of the fridge cabinets but cutting underneath it so it’s still hidden there was ever any demo?

Pull the end cabinet, cut out the bottom drywall and look around with a flashlight. Reinstalling the cabinet will cover the hole.

Great idea! Thanks Joseph

Or just cut a hole in the end of the soffit - repairing a hole in the drywall is a lot less work than removing the cabinet.