I have made a custom texture pack where, If I rename a diamond sword to Undying, it will have a custom texture.
My path file is

C:\MultiMC\instances\Fabric 1.19.minecraft\resourcepacks\Custom Textures for Undying\assets\minecraft\citresewn\cit

I have tested this resource pack on Optifine, and there it works perfectly (Please note that I change the citresewn to optifine when I am using the resource pack with optifine)
Now when I use fabric with citresewn it simply doesn't change the texture from a diamond sword to my custom texture.
pack.zip

Heres a log file from using it and photo of my mods folder
latest.log

You're specifying the texture incorrectly.
You probably meant to use:

texture=undying_sword