That’s a lot of work for a little light. Is there no such thing as small window that could be installed between the studs without compromising the integrity of the wall?

Get an electrician in to add more lighting. 1 central fixture is the worst possible type of kitchen lighting.

You would get very skinny 12" vertical openings if you went between the studs. Like sidelights to a front door, without the door. That doesn't move all the other stuff in the way either. Or fix the sheathing or diagonal bracing, if that exists in that wall. You would still need to do that. Plus, you would need custom windows, if you did not want that to be a pass though opening.

Load bearing walls often have door openings in them, they aren't always solid walls. A window sized opening does not always mean a beam.

Is this one story house? A ceiling to roof installed Solatube would bring in tons of natural light & they can also have electic lights in them for night time, That means you can use the ceiling hole for an existing electric fixture & swap for a Solatube. I have both kinds in my home. Much, much less $$ that all the dry wall work needed for window & less drastic than losing wall space. Here’s a 10” tube in my kitchen with all lights on..

Here’s lights off. My kitchen has no windows - adjoining dining area has north & east facing windows with very tall 90’ at least Douglas Firs on adjoining property blocking morning sun.

Yes, a load bearing wall should always have a header/beam to support any studs that are removed.

Yes, it does not mean replacement of the entire wall. You could get a 30" opening by the removal of one stud and replacement with a header.

What lighting do you have in your kitchen now?

You can reframe the wall like you would for any window. Framing Basics: From Windows to Doors - The Inspiring Investment

That'll help during the day. A good lighting plan with task lighting over the work zones will still be necessary.

Instead, you could replace the half lite back door with a full lite door and paint the walls a lighter color. A very pale green or a greenish white. Select a color with a high LRV (light reflectance value.) LRV ranges from 0 (black) to 100 (white). If you know the current color & brand, you can look up the LRV of the existing paint & get an idea of how much you can improve if you select a high LRV color.

The Malinois does not look impressed.

Neither does the cat!

Cats never do. That's a given.