If you look at the top of the Gimp window, you can see that the imported image is in Indexed mode. That means there are a limited number of colors defined in the image up to a maximum of 256.
The colour you want is not available so you get a replacement colour substituted.
Use menu
Image -> Mode -> RGB to change the mode.
Do all your editing in RGB mode. Save in Gimp .xcf format until 100% complete and then if required (maybe for a game of some sort) change the mode back to Indexed. Not all image formats can be Indexed mode, the common ones for Export are png and gif. see:
https://en.wikipedia.org/wiki/Indexed_color
There is a added issue. To paint in white you need to change the foreground (FG) color to white. It is showing violet in the screenshot. To change the color, click in the icon, get the Change Color dialogue, and set to white. Edit: Ok, you did that in the video, but review the docs anyway.
see:
https://docs.gimp.org/2.10/en_GB/gimp-to...color-area
and
https://docs.gimp.org/2.10/en_GB/gimp-di...lor-dialog