Very sorry for your loss - lost my mother earler this year so I have some idea of what you're going through.

My own view of your question is, sure it can be done. We live much more informally than was the case a generation ago, so many of us no longer have formal dining rooms but still want to enjoy a bit of gentility from time to time. Bring out the formal tablecloths and fine cutlery, the wine decanter and the good china, and go for it!

I’m wondering partly what makes it work when it does. In sunnydrew’s room I think it helps that although it is an eat-in kitchen, the chairs are not a super casual style?

If you are talking about very open spaces that eschew "formal" dining
rooms , it's fresher to concentrate on ambiance/texture. A runner
instead of a cloth. Votive candles versus candlestick type holders.
Seasonal but relaxed formality.Even a porch can feel very special and
make guests feel welcome..That's a trend even IN formal dining spaces
with more relaxed settings atop the table.

Having downsized into a smaller and more casual life style, I can speak from experience. There is nothing formal about my current home, but I will use any excuse to set a beautiful table. Whether the occasion is inside or on the patio. And my guests love the special touches. I give equal attention to their comfort and it's a satisfying experience for everyone. A formal table setting really does add to the experience. I think this is especially so in a casual home because it is such a welcoming combination. It signals to my guests that they deserve some extra effort on my part. Don't overthink it, just do it and enjoy it.
Sorry I don't have any pictures.

Just noticed your speculation If more formal chairs are the key.

If your goal is to achieve the "look" of a formal then .... yes... But ......you are already working with an setting that is not a formal dining area. So I would not put much effort toward acquiring formal style chairs if they do not fit overall.

However you bring up an important area -- that is, the seating choice is important regardless of style. You will want COMFORTABLE seating.

Here's what works for me:

--A pretty and well thought out table setting to set the tone from their arrival that this is a special time together. (And even if the guests do not notice the table I do, and it pleases me)
--A menu selection that is agreeable to your guests tastes and preferences. Tried and true recipes that are simple yet elegant.
-- An atmosphere that is one of comfort* - enjoyment of food, ease of conversation, and seating that is comfortable and inviting so that your guests want to linger around your table.

*a formal table setting promotes comfort because everything your guest needs for the meal is at their fingertips. Even if the guest does not use the salad fork, the bread plate , or even the wine glass it's there waiting for them.

So sorry for your loss PirateFoxy. I don't have pictures but that is exactly what I am trying to achieve with our renovation, I think it's the best of both worlds. We are taking down the wall between kitchen and dining room and planning to keep the dining room intact as our eat-in area of the kitchen. I never have understood why kitchen eat in areas are so 'cozy' and always nestled in front of doors and doorways! Maybe it's because we are a family of 6 but we never have enough space at the table!

I think I’m looking at the chairs because often eat-in kitchen furniture is quite casual in style and I find that visually jarring with a formal table setting. With the death of my dad we are considering moving in to their house, and one possibility would be to remove the wall between kitchen and dining room, since the kitchen is current a bit claustrophobic. However I do like setting a nice table. So I wouldn’t want to end up with something that felt weird because of the contrast between the kitchen and the dining area.

I suppose more formal style cabinets would help, Too. (As opposed to going very farmhouse, for example.)