Only way you can do what you propose is with the log manufacturer's engineer's stamp, along with your code official's approval...or with and independent structural engineer's design along with your code official's approval.

You need to start with a Kitchen Designer and their contractor. They will bring in a structural engineer if needed. If you have a whole floor plan, it’s easy to armchair guess it from here. If it’s parallel to the main ridge, chances are good that it is load bearing. But even if it’s crosswise to the ridge, it could be load bearing. Joists change direction and bearing wall points 4x in my own simple house. It requires an expert in person to inspect all of everything. But removing that wall means replacing all of the floors that touch it. Figure $10-$20 a square foot for that work. Plus the cost of the electrical, HVAC and plumbing relocation. 2K-5K. Plus the cost of the wall removal itself, and any needed structural additions to make that happen. $5-15K. Removing the wall itself is not that expensive if you’re already planning all of the rest on the list. If you aren’t, then it’s going to be cost prohibitive to do.

While it’s true that you need an on site inspection by a structural engineer to absolutely determine the answer, I think the likelihood that those are load bearing is in the 99%+ range. Given the spans involved and the placement, I can’t see that these are simply ornamental. The likelihood is that the architect wanted an open plan and tried to disguise these intrusive, but essential, columns by making them look ornamental. Based on where you live, costs for remodeling like this can vary widely, but, even if you are in a lower cost area, I don’t see how this could be done within a $5K budget. Besides the cost of materials and the labor, the repairs to the walls and ceiling, the re-painting, and how you will fix the holes in the floor after the columns are removed will run up the costs of what seem like a modest project. I know this isn’t the answer you were hoping for, but I think it’s a realistic one.

I think your hood is firmly attached to the wall. IMO the corbels are decorative.