Conclusion: A modern obs-studio cannot be used on a Pi400/Pi4B without an external graphics card since the required OpenGL version 3.3 isn't provided by the VideoCore VI.
Using media-video/obs-studio-27.1.3-r1 on a Pi400 fails with the message:
error: X Error: GLXBadFBConfig, Major opcode: 151, Minor opcode: 0, Serial: 32 error: Failed to create OpenGL context. error: Failed to create context! error: device_create (GL) failed error: Failed to initialize video. Your GPU may not be supported, or your graphics drivers may need to be updated.
NOTE: OpenGL 3.3 or later is required to use OBS Studio on Linux. You can check what version of OpenGL is supported by your system by typing glxinfo | grep "OpenGL" on Terminal.
glxinfo | grep "OpenGL"
OpenGL vendor string: Broadcom OpenGL renderer string: V3D 4.2 OpenGL version string: 2.1 Mesa 21.2.6 OpenGL shading language version string: 1.20 OpenGL extensions: OpenGL ES profile version string: OpenGL ES 3.1 Mesa 21.2.6 OpenGL ES profile shading language version string: OpenGL ES GLSL ES 3.10 OpenGL ES profile extensions:
https://www.raspberrypi.com/news/vc4-and-v3d-opengl-drivers-for-raspberry-pi-an-update/ : "At present, the V3D driver exposes OpenGL ES 3.0 and OpenGL 2.1. As I mentioned above, the VideoCore VI GPU can do OpenGL ES 3.2, but it can’t do OpenGL 3.0, so future feature work will focus on OpenGL ES."