OpenGL max version

I need to use a software with OpenGL 3.2, using the command :
MESA_GL_VERSION_OVERRIDE=3.2 {command_to_launch_program}

I wanted to check the compatibility before launching this. I got the following result :
$ glxinfo | grep 'version' server glx version string: 1.4 client glx version string: 1.4 GLX version: 1.4 Max core profile version: 4.3 Max compat profile version: 3.1 Max GLES1 profile version: 1.1 Max GLES[23] profile version: 3.1 OpenGL core profile version string: 4.3 (Core Profile) Mesa 20.3.5 OpenGL core profile shading language version string: 4.30 OpenGL version string: 3.1 Mesa 20.3.5 OpenGL shading language version string: 1.40 OpenGL ES profile version string: OpenGL ES 3.1 Mesa 20.3.5 OpenGL ES profile shading language version string: OpenGL ES GLSL ES 3.10 GL_EXT_separate_shader_objects, GL_EXT_shader_implicit_conversions,
I have a few questions :

  • What is the difference between « Max core Profile » and « Max compatible profile » ?
  • Why is my GLX version 1.4 whereas it seems it can go up to 3.1 easily ?
  • What is the risk of launching the software, forcing OpenGL 3.2, knowing that the max compat profile is 3.1 and the max core profile is 4.3 ?
  • How can I make the max compat profile improve to 3.2 or more ?

Thanks for your help,
Have a nice day,