Local python variables are not defined when using `py3eval` from within a separate python file

First of all, I apologize if this is not the right place for this question.

Let's say I have the following python code:

import vim
x = 1
print(vim.eval("py3eval('x')"))

Now I use this code in a vim function in the file myplugin/autoload/myplugin.vim:

function! myplugin#myfunction()
python3 << EOF
import vim
x = 1
print(vim.eval("py3eval('x')"))
EOF
endfunction

Calling this function from vim or lua (vim.fn["myplugin#mytest"]()) prints 1 as expected.

However, I get an error when I try the following:

create a file mymodule.py in the folder python3 in my plugin root directory with the following contents:
```
def myfunction():
import vim
x = 1
print(vim.eval("py3eval('x')"))
```
run vim.cmd('py3 import mymodule')
run vim.cmd('py3 mymodule.myfunction()')

I get the following error:

NameError: name 'x' is not defined

I expected both implementations to work exactly the same (it should not matter whether the code is defined in a python3 << block or in a separate python file). Why is x not defined in the second case?

Edit: changed pyeval to py3eval

neovim / pynvim

Local python variables are not defined when using `py3eval` from within a separate python file #501