Command works when path is entered manually, but not when $PATH is used

Question

I installed Golang into a custom folder under $HOME called .go/exec. After the installation, it put the binary under $HOME/.go/exec/go.

So I updated $PATH to contain this directory: $HOME/.go/exec:$PATH.

Here is the question:

When I execute a command by entering the path manually, it works without any issues:

~/.go/exec/go/bin/go version

However, with $PATH it does not work:

go version
# zsh: permission denied: go

I am logged in with $USER, and seems like permissions are set correctly. Here is a namei output:

pwd
# /home/user

namei -olm ./.go/exec/go/bin/go

drwxr-x--- user user .
drwxrwxr-x user user .go
drwxrwxr-x user user exec
drwxr-xr-x user user go
drwxr-xr-x user user bin
-rwxr-xr-x user user go

Could anyone guide me where the issue is?

I thought just adding the top directory to $PATH should have been enough, am I wrong?