How to convert from Downdraft cooktop range to hood
Without a photo of your existing setup we can do a little guessing. It sounds like you are on a wall not an island with cabinets over the counter.
The main part of installing a hood (or possibly a over the stove microwave/ hood combination) are the same removing cabinets if on a wall and the exit location , through the wall or into the attic and thru the roof.
You have identified the cabinet modification will be needed , how close are we to a window? With exterior wall stoves going out the wall is the easiest/ cheapest way to go, interior wall through the roof. I mentioned the microwave/hood option because modifying the cabinets will be the most expensive part so I basically eliminate the cabinet and have the microwave there, as far as modification this ends up being a plus for selling if you do not already have a built in microwave.
Modifications all depends on the spacing above or how the cabinets are built 1 piece built in place can be modified but will be the most expensive option. If your cabinets are segmented (most common) and the segments are split on each side of the stove all options are open. Installing a low profile hood not that hard moving the bottom of the cabinet up a foot adding some brushed stainless , copper or brass cladding on the cabinet sides and behind the stove top a lady catcher when selling.
Similar with the microwave option but less cabinet repair (shorten the doors etc)
These are the things I have done on flip and my own homes currently moving from downdraft island to wall overhead hood.
The homes I added the overhead microwave where there was not one really helped them were not high end homes but this really helped the sale.
On one home we installed a low profile vent hood and modified the cabinet then used hammered copper cladding on the cabinets and behind the stove, I thought it looked nice but we ended up with multiple families bidding on that 1950’s cracker box house and it sold above our asking and the realtor said it was the kitchen. New matching appliances sink and that cladding were all we really did.
There are lots of options and a couple of us that have done remodels could be more helpful with a photo.