Running Python script in C# without installing Python environment

It is possible to run the script without having an environment installed on your users machine. You will however still need some libraries installed, so the answer to your question is yes and no -

These links should point you in the right direction -
How do I run a Python script from C#[^]
Steps - How to call a Python function from C# using the .Net library[^]
Calling Python from C#: an introduction to PythonNET[^]

You mentioned that you used the Python.NET library, the below steps worked for us -
1. Install the Python.NET library from Visual Studio, right-click on your project, select "Manage NuGet Packages," search for "PythonNet.
2.Import the namespaces in your C# code -

using Python.Runtime;

3. Initialize the Python runtime -

using (Py.GIL()) 
{
    PythonEngine.Initialize();
    // ...
}

4. Execute the Python script -

using (Py.GIL()) 
{
    PythonEngine.Initialize();
    PythonEngine.Exec("print('Hello, Python!')"); //sample...
//your actual Python script content goes here...    
}

5. Clean up after execution -

using (Py.GIL()) 
{
    PythonEngine.Initialize();
    PythonEngine.Exec("print('Hello, Python!')"); //sample...
//your actual Python script content goes here...
    PythonEngine.Shutdown();
}

Note that the Global Interpreter Lock (GIL) block (See links) is required to allow Python code to execute