Why two posts on the same topic?

For some reason you posted twice, you should delete this one.

The wood in your inspiration photo isn't oak. It's knotty wood alder with a custom blended stain per the builder's Q&A for that photo. With raised panel cabinetry like in your kitchen, that would be a very tedious DIY if you're not experienced in the multi-step process or a cost-prohitive professionally done restaining. I'm not sure darker cabinetry would have enough contrast with the dark counters unless you're revamping your lighting.

There are 2 kinds of dark wood in the kitchen, which has a sense of the times

I doubt you have the free time to properly sand all the surfaces of your cabinets to take stain and then finish. Both sides, Danielsen. General Finishes has the products to diy the job successfully. How To Finish Wood: Painting and Staining Instructional Videos | General Finishes

To me, the stain in the last picture looks pretty much the same as the stain in the first pictures. The only difference is the knotty wood which makes it look darker.

I wouldn't refinish to do a dearker stain. If you want a different look, I'd paint the cabinets instead.

I haven’t done it myself, but I recall some posters having good luck darkening oak cabinets with gel stain. google that and you’ll find the recommended brands and methods. Good luck!

If you strip the poly you can get them darker. Oak does not paint attractively IMPO.

Just be careful what you wish for. Here our dark oak kitchen before we lightened up.

Oak takes stain easily, and pretty evenly. It’s a great project, and doesn’t require anything special to make it work. Minwax oil based or gel stains should be fine as long as you can find a color that you like. General Finishes has a brown mahogany you might like. Just sample them and choose. Otherwise you’ll be mixing stains or playing with dyes and glazes, and that’s much less straightforward.

If you’re trying for that mahogany stain on the island of your inspiration images, just know that the grain on oak is absolutely going to show, especially on the fireplace on that highly grained piece of wood up top.

That said, it might be best to start with the fireplace. Kitchen cabinets require a lot of prep and once you start working on them it’s tough to stop. There are lots of tutorials online. Find a good video, read a few wood finishing web pages. you should be grand. Good luck!

Also, you can practice on the inside of cabinet doors to see how any product will look on YOUR cabinets. Since you won't be doing anything outrageous (it appears) anything you do will probably not be very noticeable, or will be redoable/fixable when you settle on your desired finish.