Repository: neovim
Issue: :checkhealth should detect if `g:loaded_python3_provider=1` was wrongly set
Labels: bug,provider,complexity:low,checkhealth

### Problem

When I try to run a Pyhton expression, I get that there is not python provider:

```
:lua vim.fn.py3eval("2+2")                                                                                                               
E5108: Error executing lua Vim:E319: No "python3" provider found. Run ":checkhealth provider"                                            
stack traceback:                                                                                                                         
        [C]: in function 'py3eval'                                                                                                       
        [string ":lua"]:1: in main chunk
```

However there is.

Here is the output of `:checkhealth provider.python`:
```
provider.python: require("provider.python.health").check()                                                                           
                                                                                                                                        
 Python 3 provider (optional)                                                                                                         
 - pyenv: Path: /usr/share/pyenv/libexec/pyenv                                                                                        
 - pyenv: Root: /home/USERNAME/.pyenv                                                                                                 
 - Using: g:python3_host_prog = "/home/USERNAME/.pyenv/versions/neovim/bin/python3"                                                   
 - Executable: /home/USERNAME/.pyenv/versions/neovim/bin/python3                                                                      
 - Python version: 3.11.7                                                                                                             
 - pynvim version: 0.5.0                                                                                                              
 - OK Latest pynvim is installed.                                                                                                     
                                                                                                                                       
 Python virtualenv                                                                                                                    
 - OK no $VIRTUAL_ENV                                               
```





### Steps to reproduce

1. Create a virtual environment with pyenv: `pyenv virtualenv 3.12 neovim`
2. Activate it `pyenv local neovim`
3. Install pynvim on it: `python -m pip install pynvim`
4. Set the virtual environment as python provider in init.lua:
```
-- WARNING: A python 3 provider is needed for zotcite
vim.g.loaded_python3_provider = 1
-- WARNING: Path must be set to a `python3` executable file,
--          NOT to a `python` executable file.
--          That won't work.
vim.g.python3_host_prog = MYHOME .. "/.pyenv/versions/neovim/bin/python3"
```
5. Run `:lua vim.fn.py3eval("2+2")`

### Expected behavior

neovim should not error out as it says the provider is present

### Neovim version (nvim -v)

v0.10.1

### Vim (not Nvim) behaves the same?

no

### Operating system/version

Arch Linux

### Terminal name/version

kitty 0.36.1

### $TERM environment variable

xterm-kitty

### Installation

Arch Linux official package