Just using the Hidden Carina Nebula texture pack isn't enough, you need to find the texture and use it to replace the end sky texture using the instructions near the bottom of the page.
Version 1.2 works with optifine, though version 1.3 doesn't work with current versions of optifine and forge.
Version 1.1 doesn't work with optifine, so if you want to use it with optifine, you need either version 1.2 or version 1.0 of the mod. You can find version 1.0 under the "files" tab above. Also, there are different instruction on how to prepare the resource pack for version 1.0.
Fabric version here.
Use with a resource pack! It won't work without one that adds a custom end sky.
I made a resource pack here that uses the custom sky without having to edit the resource pack:
For version 1.2 and 1.1:
Unless you are using the resource pack that I made, you need the file assets/minecraft/textures/environment/custom_end_sky.png to be a custom sky image from a custom sky resource pack, which you can find in the assets/minecraft/optifine/sky/world0 folder. It isn't necessary, but if you don't add the file, the end could look like the picture above.
For version 1.0, the file needs to be named end_sky.png instead of custom_end_sky.png
When using version 1.0, it could make the end sky, look weird if you either use only the resource pack, or only the mod. I recommend using the mod with the resource pack, though no major bugs/glitches would occur.