The minecraft 1.18 (exact) version on fabric requires the following versions for the fabric loader, fabric itself, and yarn_mappings:

minecraft_version=1.18
yarn_mappings=1.18+build.1
loader_version=0.16.10

# Fabric API
fabric_version=0.44.0+1.18

However, when I tried any of these versions, I get the following error:

[main/ERROR] (FabricLoader) Incompatible mods found!
net.fabricmc.loader.impl.FormattedException: Some of your mods are incompatible with the game or each other!
A potential solution has been determined, this may resolve your problem:
         - Replace 'Minecraft' (minecraft) 1.18 with version 1.18.1.
More details:
         - Mod 'Fabric API' (fabric) 0.46.4+1.18 requires version 1.18.1 of 'Minecraft' (minecraft), but only the wrong version is present: 1.18!

When I simply remove the references to cloth-config in build.gradle, it uses the correct version of Fabric API again (0.44.0+1.18). Is there maybe a dependency to the faulty version?
Thank you!

Just solved it by combining them, as such when adding the mod to build.gradle:

    modApi("me.shedaniel.cloth:cloth-config-fabric:${project.cloth_config_version}") {
        exclude(group: "net.fabricmc", module: 'fabric-loader')
        exclude(group: "net.fabricmc.fabric-api")
    }

Hopefully this can help someone if they run into the same issue!

Also, I am adding the mod to my dependencies as such:

    modApi("me.shedaniel.cloth:cloth-config-fabric:${project.cloth_config_version}") {
        exclude(group: "net.fabricmc", module: 'fabric-loader')
    }

I know it deviates slightly from what is recommended in the documentation, but otherwise it was throwing the following exception:

java.lang.IllegalStateException: duplicate fabric loader classes found on classpath ...