Spout sharing breaks when going fullscreen

[merumerutho]

OS: Windows 11
LOVE version: 11.4

How to reproduce:

• Run with Spout sender enabled
• Start with patch "demo_17"
• Verify that Spout sharing works properly
• CTRL + ENTER to go full screen
• Spout sharing hangs after some frames
• Going back to windowed mode does not fix the issue

I suspect it's bound to the love.window.setMode function actually destroying and recreating the GL context.
Updating the Texture ID continuously does not seem to fix the issue. It seems like the Texture ID switches to 0 for whatever reason (becomes invalid?)