The LVP mfg. should have a matching stair nosing for it.

If your LVP manufacturer doesn't have a matching piece, you can either (i) try to find another similarly toned LVP that has matching stair nosing, or (ii) use a solid wood piece of stair nosing. I assume that various species of wood have stair nosing available - I've seen stair nosing in red and white oak for sale.

EDIT - quick search found these:

Thank you!

If your LVP manufacturer doesn't have a matching one, it really seems like you'd be able to find a close match in another LVP (there are so many shades of brown in your LVP).

However, if you don't, you can play around with some stains on scrap wood to make something that's close - you could mix some different ones to find a shade that's in your LVP + works with the carpet on the stairs (your carpet appears to be fairly new - so, I assume that you aren't replacing it). It will "disappear" more if you select a color that works with both.

FYI - Here are a few tips on how to keep the carpet on the middle section of your stair tread looking as nice as on the sides of the tread.

https://www.tiktok.com/@athomewith_anna/video/7052699673433263366

She goes a little overboard - but her tips re: using a carpet rake and/or fork do work.