I tried with custom item and it didn't work

I also tried with tags, it doesn't work either

Swords list:

durasteel
hallowed
mythril
orichalcum
osmium
palladium
prometheum
quadrillum
runite
star platinum
steel
legendary

versions: mythicmetals-0.18.2+1.20
levelz-1.4.11

I think you might just be creating the datapack wrong. I just managed to create this myself using the following data from the example datapack on GitHub

I think what you are doing wrong is in the first image provided you added a required field, which I do not believe is valid. In the second example it might be true it does not work because of tags, although I am unsure what the documentation exactly means with this. It is not clear whether you need to specify a tool/armor material, the type of item, and also add said item to a specific tag? (Maybe c?)

I recommend having logs open while developing datapacks. They usually throw error messages if the JSON parsing specifically is invalid. Anyhow, I can confirm this data structure with custom item works, with the side-effect of not disabling the right-click ability of Legendary Banglum Tools (I assume it does not check for using tools on blocks vs. using an item for the skill check, I advice opening a separate issue for this).

{
    "replace": false,
    "skill": "strength",
    "level": 14,
    "item": "minecraft:custom_item",
    "object": "mythicmetals:durasteel_sword"
}

This is my first datapack, I don't really know what to do, the required in the first image was just an attempt that I took from one of the compatible items already present, copy your code and it still doesn't work

If you can help me figure out if there's something I'm doing wrong, I'd appreciate it.

Are you still experiencing this problem? I don't think this is an innate issue with Mythc Metals itself, but this is more likely an issue you are facing while creating your datapack.
For now I will close this issue. If you still need support surrounding it, I suggest joining our Discord Server, as it is much easier/faster to help you this way.