Opinion on how far bull nose should extend on the side of stairs?

Stairs are coming along nicely, I'm actually taking much longer than expected since my staircase isn't 100% 90 degrees on the sides and I have to cut each tread accordingly and then shape it to fit... it's a tedious process but the results are zero gaps and I will not have to caulk the sides to cover up shoddy work.. I am at the point of the bull nose for my two small landings going down to the basement.

Should the bull nose go all the way to the sides past the stair case walls or should they stay within? All the step treads are within the stair case. But, one thing I am noticing if I do it that way the tops of the landing will have this weird gap that the vinyl plant floor won't meet up to the bull nose. The bull nose would be the only part that extends slightly past the frame (sides/not sure the proper terminology) of the step walls.

1. 1st picture shows the gap from the top of the landing hitting the side of the frame of the staircase. To it's left you see a baseboard. *Note these are NOT the baseboards I am using they are simply a test to make sure I keep the 1/4 gap all the way around and it's covered but I am putting new baseboards on top of the floor. No shoe trim molding will be on the bottom of the baseboard.

2. 2nd picture shows the gap that would be left and you would see the bottom tongue of the vinyl plank. Note that the tonge part has to go under the bull nose which prevents any type of "gap" or seam. If I just but it up against the bull nose it doesn't look right.

3. 3rd picture shows what I am talking about in the description of picture 2. Weird ass gap.

4. 4th picture is what I am proposing in terms of notching the side of the frame/stair wall (1/2"ish) so that the bull nose can slide all the way to the wall.

*IGNORE*5. 5th picture just shows a closer view. It would not be lifted like that if I notch/mark the stair and cut a rounded cutout to follow the bullnose profile.

6. 6th picture shows baseboard test that would sit above the floor and most likely the bullnose.

7. 7th picture is of the right side of the stair case. You can see the weird gap but this time no gap on the floor... simply the bullnose to the stair wall.
*I would think if I notch the left side I should follow suit on the right side so it doesn't look odd. I would ALSO undercut that piece of wood so that the floor goes under it, just like I have been doing for door trim..etc..

8. 8th picture is of the right side but sliding the bull nose all the way to the right.

So just asking opinions on what would be best. I don't want to structurally make the stairs worse if doing that is a no-no...etc. That why I wanted to ask. I couldn't find any information online anywhere about this. I will note that I actually filled in all the notches on the stairs were the stock treads were into the sides. Now looking back I don't think I should have done these two landings like that but it's nothing a dremel can't really take care of quickly with the wood putty I used.

Appreciate all the help! I hope I am making sense, lol.

Attached Images
File Type: jpg 1gap.jpg (148.6 KB)
File Type: jpg 2gap.jpg (150.6 KB)
File Type: jpg 3gap.jpg (128.4 KB)
File Type: jpg 4NOgap.jpg (150.1 KB)
File Type: jpg 6baseboard.jpg (135.9 KB)
File Type: jpg 7rightsidegap.jpg (146.3 KB)
File Type: jpg 8rightsidenogap.jpg (131.7 KB)

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