I attempted compiling curios at run time but for some reason it doesn't appear in game. Gradle compiles with no errors and I also have the correct repository.
This is in the repository block,
maven { url = "https://maven.theillusivec4.top/" }
And this is in the dependencies block
runtimeOnly fg.deobf("top.theillusivec4.curios:curios-forge:1.17.1-5.0.0.1")
I also tried using implement instead of runTimeOnly but still produces same results.
I'm using:
ForgeGradle: 5
Forge: 37.0.44 (official mappings)
(I can also reproduce it with version 5.0.0.0)

I can also see the deobfuscated jar in my libraries.

This is a Forge bug, should be fixed when MinecraftForge/MinecraftForge#8064 gets merged.

Edit: For reference, the current workaround is to add this to your build.gradle with the relevant Forge version:

minecraft.runs.all {
    property 'ignoreList', "bootstraplauncher,securejarhandler,asm-commons,asm-util,asm-analysis,asm-tree,asm,client-extra,fmlcore,javafmllanguage,mclanguage,forge-1.17.1-{version},1.17.1-forge-{version}"
}

I am running into the same problem - deobfuscated libraries are available (in the correct version) in IDE, but at runtime Curios is not available. If adding it as a dependency in mods.toml forge shows an error for the unmet dependency, if not putting it in toml it fails once the first class is loaded.

build.gradle:

curios_mc_version=1.17.1
curios_version=5.0.0.1
...
compileOnly fg.deobf("top.theillusivec4.curios:curios-forge:${curios_mc_version}-${curios_version}:api")
runtimeOnly fg.deobf("top.theillusivec4.curios:curios-forge:${curios_mc_version}-${curios_version}")

Forge Version: 1.17.1-37.0.50 with parchment mappings

It looks like this has been resolved as of Forge 1.17.1-37.0.75.