If you're not replacing the cabinets, leave the soffits. There is nothing to be gained by removing them. If you did that you would then have an empty space that needs to be dusted. If you want ideas for a budget remodel, post pictures of your space.

My step son took the soffit out of our kitchen and I put my collection of roosters and red vases up there. We took out the ceiling fan and put an ordinary light fixture in. Made my kitchen seem bigger and brighter. Everyone comments on how they love my kitchen. We did nothing with the cupboards, they are stained light and have brass knobs. If you don't want to dust, line the top of your cupboard with wax paper. Just toss the wax paper and put more down when it gets dusty.

Do not remove the soffits only to leave a space for stuff (or nothing). Both will collect grease and grime.

Posting photos will get you more advice...

Just echoing some other comments, for emphasis. Do not remove the soffit if you are not changing the cabinets. Plus, do you know that the soffit is empty? Or could it have plumbing, gas, or electrical lines in it? Or ductwork? But even if empty, the idea of taking the soffits down just to put stuff on top of the cabinets is not an improvement.

There are many other ways to update a kitchen. Post a photo. But typically we see 90s kitchens have fussy window treatments, dull cabinet knobs, and bad lighting. So before even any major changes, just changing those will help. Also typically backsplash and counter are easier to replace and have a greater impact than painting cabinets. If your cabinets are old and have for example the arched doors, no paint is going to disguise that, and may make it look worse.