Most of the [I hesitate only slightly to call them clickbait] recipes for chicken noodle soup using only a chicken breast make up their entire flavour profile using ready-made stock. The chicken breast is nothing more than something to look at, a bit of decoration so you can call it chicken soup. It will add very little flavour to the soup at all.
To really make it from scratch you need to start with either a whole chicken [quartered], or even less fuss, a carcass left over from yesterday's roast dinner, optionally plus your single raw breast to add at the end, for some 'chunks'. Personally I'd just make sure I started with enough meat left on the carcass & skip the fresh at the end. Alternatively, add a couple of fresh thighs cooked as long as the carcass. Fresh thighs will get tender over time, fresh breast will become like so much pencil eraser.
The 'body' of your soup will really come from the 'bits you don't eat' - the skin, bones, cartilage etc. This will develop not only a much deeper flavour, but texture & mouth-feel, it will naturally slightly thicken the soup.
Throw the carcass in with any or all of - onions, celery, carrots, garlic, fresh thyme, parsley, salt & black pepper [&/or anything in the fridge that needs using up].
Simmer until it completely falls apart - call it three to four hours. This is one of those things it's pretty hard to over-cook, so don't be in a hurry. You can play with your final flavour profile by reducing at a boil or adding water. [You lose less if you make it a little strong & have to knock it back, of course. Boiling boils off a part of the flavour - you can smell it in the room], also check seasoning part-way & again at the end.
Lift out all the bones, skin, anything you don't want in the final soup, shred any remaining chicken into easily spoonable sizes.
Dice your fresh chicken if you are using it, and add with or after your noodles, depending on how long the noodles need.
Fresh diced chicken breast takes about 2 minutes; most people over-cook it [pencil erasers again]. Check one of the largest pieces for doneness.
If you leave out the fresh breast, your soup will freeze nicely, with or without the noodles.