Will the Fabric have something like Ore Dictionary (as in Forge)?

does Forge still even have oredict in the newer versions?

Fabric has tag conventions

No sense in implementing something Vanilla already has.
I'm pretty sure Forge itself also yeeted oredict in favor of tags.

Yep, Forge has things like forge:ores/iron, while with Fabric we use c:iron_ores

(Actually iron ores may be a vanilla thing, I haven't checked)

I tried to do it like this:
https://github.com/CottonMC/CottonResources/blob/1.15.2/src/main/resources/data/c/tags/items/aluminum_dusts.json
https://github.com/CottonMC/CottonResources/blob/1.15.2/src/main/resources/data/c/tags/items/aluminum_dust.json
But:

[22:52:55] [main/ERROR] (Minecraft) Couldn't load item tag c:sand_dust as it is missing following references: c:sand_dust (from SandProject)
[22:52:55] [main/ERROR] (Minecraft) Couldn't load item tag c:sand_dusts as it is missing following references: c:sand_dust (from SandProject),#c:sand_dust (from SandProject)

well, of course, you need to define the tag

src/main/resources/data/c/tags/items/sand_dusts:

{
    "replace": false,
    "values": [
        "yourmodid:youritem"
    ]
}

sand_dusts:

{
  "replace": false,
  "values": [
    "sandproject:sand_dust",
    "#sandproject:sand_dust"
  ]
}

sand_dust:

{
  "replace": false,
  "values": [
    "c:sand_dust"
  ]
}

[23:13:05] [main/ERROR] (Minecraft) Couldn't load item tag c:sand_dust as it is missing following references: c:sand_dust (from SandProject)
[23:13:05] [main/ERROR] (Minecraft) Couldn't load item tag c:sand_dusts as it is missing following references: #sandproject:sand_dust (from SandProject)

I don't understand why cottonmc has "c:tag" tags everywhere and everything works (otherwise the developer changed it), but it doesn't work for me

what are you doing here, just do:

{
  "replace": false,
  "values": [
    "sandproject:sand_dust"
  ]
}

Assuming sandproject:sand_dust is your item's name

For modding support, I would recommend visiting the Fabric discord server: https://discord.gg/v6v4pMv