I solved the issue.
Though the message:
There was a problem reading the entry module-info.class in the jar C:\...\asm-analysis-6.2.jar - probably a corrupt zip
Was not the problem that led to the crash at the end of the log I provided which was the error:
net.minecraftforge.fml.common.LoaderExceptionModCrash: Caught exception from Forge Mod Loader (FML)
Caused by: java.lang.NullPointerException
More likely the problem is that Intellij 2023 doesn’t download the dependencies provided in the build.gradle automatically anymore.
For me the easiest fix was to downgrade to Intellij 2021 but I think anything under 2023 will also work.
For more information about this particular issue can be found here: https://github.com/quat1024/modern-forge-1.12-template/issues/2