Just so I'm clear, is this the current layout:

Here are some layouts with builtin seating:

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I would talk to a couple of CKD at some local cabinet shops. They have the expertise to help you figure this out. (Not HD or Lowe's)

Forgot to post this one. You'll have to confirm the measurements with your kitchen designer or cabinet maker but this might be a way to incorporate your existing table.

Creativity costs. It is not free. How much have you paid as a design retainer? $1500? $3000? $6000? How much are you willing to spend to remodel the home? 100K? 200K? 400K?

How about this: knock down the dividing wall between the living room and kitchen, except for as much is needed for the fridge. Add a little bit of wall on the other side, namely just as deep as the adjoining wall is before it becomes the door. At this wall place lower kitchen cabinets, a counter top and then upper kitchen cabinets, so you can store a lot (for your seem to have a lot of stuff). But leave a space of about 3 feet open at the end near the doors for the dog's food and water. Don't ever again let the microwave become a wart on the kitchen's face.

Place a L-shaped kitchen, starting to the right of the doors, then around the corner up to the bit of wall you left in place (as to not have to watch the sides of the kitchen). Make sure your waste bins are in the kitchen cabinets. With just a few glass doors and lighting underneath the upper cabinets it will look great.

Place your table and chairs in between and I think it will look a lot better if you get a rectangular table. Make sure the chairs go under the table. You know what we just did? We got a wooden kitchen counter that somehow matches the wooden table and wooden chairs in color. Looks gorgeous.

Also make sure that the dining area furniture matches with the living room area, since it has become one open space now.

Get the walls the same color in both area's, for this space is too small for different colors. Get the same wooden floors throughout this floor.

Oh, I'm sure it is going to be lovely. And it doesn't have to cost as much as Sophie is warning you about. The big shop from Sweden has affordable kitchens and everything else. If you can build and redo most yourselves you are still looking at 15 grand, though. With help probably 20 grand at least.

Be sure to ask the architect about knocking out that wall, for if it carries a load, you either have to leave a pillar (could be nice) or have to add a horizontal pole to the ceiling. That might cost a few grand too, for it has to be done by professionals.

If you do not have that money yet, go safe up first.

And never ever let the fridge and counter top become the clutter center of the house again.

Your budget is wholly inadequate to your stated wants. Double it, and you would still be lacking. You don’t get creativity on a budget that barely covers like for like cabinet replacement. The average kitchen remodel of 61K does not cover any changes in layout or structural modifications. The average 24K cabinet expenditure in the average 61K kitchen renovation doesn’t cover a Houzz level kitchen at all. An upscale average kitchen remodel is 125K. A Houzz level kitchen remodel with s reimagining of the space is double that.

Paint what you have with a professional. Get new appliances. New counters. Your 20K is spent.

To maximize storage, I would eliminate the corner cabinet and put the sink and dishwasher on the same wall as the stove.

Here are two pics for comparison...

I just find corner cabinets difficult to access. Also, some of the corner cabinet solutions may not function if partially under the sink.

I'm wondering if you may be better off with all the appliances on 1 wall and the opposite wall all cabinetry with an island possibly??

https://www.houzz.com/magazine/a-single-wall-kitchen-may-be-the-single-best-choice-stsetivw-vs~10980827

Removing walls can certainly be done with that budget. There just will not very much left over for the rest of the project. No one is talking high end at all. Very basic work from licensed and insured professionals who pull permits and consult the proper structural engineer is not cheap.

Now, if you are a structural engineer, and your other half is an electrician, and your brother is a flooring professional, and you own a legal construction disposal site, then your budget would be adequate for materials only for a basic DIY kitchen. But not the wall removal.

Contractors are bigly busy. Prices have risen. There's a 9-12 month waiting period for anyone good and in demand. If someone is available to start next week, you need to wonder why. They likely aren't busy for a reason.

Center walls in splits are load bearing and expensive to remove well. Well means a rec see header so there is no beam hanging down in the space further reducing the ceiling height.

My suggestion would be to have that done properly, including the needed wall/pier support required in the basement, patch the floor, and keep saving to do the kitchen project later as a separate project.

How wide is the wall to the right of the patio door?

With 82 inches, it's ridiculous not to turn the corner -- I disagree with er612 on this one. A corner kidney pull-out works great next to a sink, and you get a lot more working space between sink and stove, which is the busy spot in any kitchen. I don't think that the little island, right next to your table, is worth that. I do like all the shallow pantry on the other wall, rather than the useless desk, but I also think it's ok to have something deep over there if you like the arrangement better. Nobody actually likes a stove with just a little space before the fridge, if they can avoid it. I didn't think your walk from fridge to sink in the original drawing was too bad. Other space over there will get less use, so should be for things that hog counter space like coffee maker and toaster, etc.

Congratulations on your finished project! I'd be so interested to know if you were able to stay close to your budget.

Beautiful!!!