I'll summarize what was explained in the video someone linked under your question, as I was able to reproduce the steps and create a working C project in Visual Studio. Kudos to the video creator and kiner_shah for sharing.

As a precondition, you shall be able to create C++ project in VS, so make sure you have the right extensions installed.

Create a new project (Shift+Ctrl+N), select Visual C++ and Console App. This will create a new console app with a default c++ main file. Remove that file and put in a main.c file. This can be compiled, and works just fine.

Short answer: Yes, you need to rename .cpp files to c, so you can write C: https://msdn.microsoft.com/en-us/library/bb384838.aspx?f=255&MSPPError=-2147217396

From the link above:

By default, the Visual C++ compiler treats all files that end in .c as C source code, and all files that end in .cpp as C++ source code. To force the compiler to treat all files as C regardless of file name extension, use the /Tc compiler option.

That being said, I do not recommend learning C language in Visual Studio, why VS? It does have lots of features you are not going to use while learning C

To run a C program in Visual Studio Code, follow these steps:

1. Install the C/C++ Extension: Ensure you have the C/C++ extension installed in Visual Studio Code. You mentioned you have this set up, which is great.
2. Set Up a Workspace: Create a new folder for your C projects. Open Visual Studio Code and select File > Open Folder... to open your newly created folder.
3. Create a C File: Inside your workspace folder, create a new file with a .c extension (e.g., hello.c). You can do this by right-clicking in the Explorer pane and selecting New File.
4. Write Your Code: Write your C code in the newly created file. For example:

      #include 
      
      int main() {
          printf("Hello, World!\n");
          return 0;
      }
   

5. Configure Build Tasks: You need to set up a build task to compile your C code. Press Ctrl + Shift + B to open the build tasks menu. If prompted, select Create tasks.json file from template and choose Others. Modify the generated tasks.json file to include the following:

      {
          "version": "2.0.0",
          "tasks": [
              {
                  "label": "build",
                  "type": "shell",
                  "command": "gcc",
                  "args": [
                      "-g",
                      "${file}",
                      "-o",
                      "${fileDirname}/${fileBasenameNoExtension}"
                  ],
                  "group": {
                      "kind": "build",
                      "isDefault": true
                  },
                  "problemMatcher": [
                      "$gcc"
                  ],
                  "detail": "Generated task by gcc"
              }
          ]
      }
   

6. Build Your Program: Press Ctrl + Shift + B again to build your program. This will compile your C code and create an executable in the same directory.
7. Run Your Program: Open the terminal in Visual Studio Code (View > Terminal or `Ctrl + ``) and run your program by typing:

      ./hello
   

   (Replace hello with the name of your executable if different.)
8. Debugging: To debug your program, you will need to set up a launch configuration. Go to the Run view (left sidebar) and click on create a launch.json file. Choose C/C++: g++ build and debug active file. This will create a launch.json file where you can configure debugging settings.
9. Start Debugging: Set breakpoints in your code by clicking in the gutter next to the line numbers. Then, press F5 to start debugging your program.

By following these steps, you should be able to set up Visual Studio Code for C programming and run your code successfully.

References:

• Walkthrough: Compile a C program on the command line

The guide for using C++ with Visual Studio Code is located here:

• C/C++ for Visual Studio Code

If you are using the windows operating system, you can install the Microsoft Visual C++ (MSVC) compiler toolset as described here:

• Configure VS Code for Microsoft C++

Otherwise you should read the tutorials for the compiler you want to use:

• Tutorials for other compilers

The reason I refer to links, instead of explaining the details here, is because the answer might become outdated/obsolete. Sometimes links are better than explanations.