The linked widescreen fix from PCGamingwiki does not work, it is a newer version?
What I did to get it to work was:

1) Install the game to c:/mygames/POP
2) Download the zip from this reddit thread:
https://www.reddit.com/r/PrinceOfPersia/comments/g2m7ce/prince_of_persia_warrior_within_graphical/
3) Unzip all files from that zip into the install location (e.g. c:/mygames/POP)
4) Edit pop2.ini and set your desired resolution, I went with:
[MAIN]
Width = 3440
Height = 1440

[HUD]
HUD_posX_auto = 1 // 0 - Off; 1 - On;
HUD_posX = -0.148958 // -0.082450 - for 16x10 mode; -0.148958 for 16x9 mode;

[MISC]
HUD_glitch_fix = 1

5) Run the upx.bat file in the install location, this will update pop2.exe
6) Run the game and create a profile, it should already have your desired resolution in place (it did for me).