No dimension's. No idea on what may or what may not be load bearing. What do the elevations look like?

The typical Cape Cod has a stair and Powder Room blocking the current lifestyle concept people strive for - a Kitchen, Dining, and Living all interacting visually and adjacent to each other. The previous owner moved the Powder and apparently brought HVAC upstairs, but it is sort of 1/3-baked.

Reading between the lines, you are correct a Family Room addition off the back, with Master Suite upstairs, is a common solution to Cape Cods. There isn't a lot of info, but the word "invest" is a choice term. Reading into that word, the expense of a full remodel Kitchen can be weighed against an addition with just a refresh if budget or ROI is set.

In your proposed plan I can see the trouble of sliding the Powder allows an island, and you have a full remodel Kitchen. So you might spend $80K-$150K on a nice Kitchen, an awkward Powder/Hall, and improve to a 1/2-baked layout.

My opinion is that once costs start to soar, for essentially finishes, staying with a compromised layout with no creative opportunities begins the path to sunk cost fallacy in the future. For ROI, I prefer to get the concept right, and in the future it's easy to change finishes.

Since my comment sounded wordy and like AI, here's a sketch of what I would consider worth remodeling as "investment," so if you are completely gutting the Kitchen and Powder anyway, move them to be beneficial to most people's lifestyles: