[26.1] Move late stages of mod loading out of the first resource load

[XFactHD]

This PR moves the second and third stage of mod loading (CommonModLoader.load() and CommonModLoader.finish()) out of the initial resource reload, instead running it right before the initial reload is set up and executed. This ensures that loading errors in these stages don't cause the resource load to abort, restart in "safe mode" and then crash on completely unrelated follow-up issues, allowing us to instead capture the loading error and terminate immediately through the ELS error screen.
Moving these loading stages out of the resource reload allows us to remove the custom LoadingOverlay and therefore also (at least in theory) the "external GL texture import" extension patches.

I'm opening this as a draft for now for two reasons:

• The error handling can only be properly tested after updating LWJGL in FML
• ELS status messages in these two stages can currently not be shown because running DisplayWindow#periodicTick() after the window handover causes a weird lockup where the game seems to start fully (pausing it in the debugger ends up in vanilla GUI renderer code) but the window keeps showing the last ELS frame with the correct last status message and becomes completely unresponsive

[neoforged-pr-publishing]

• Publish PR to GitHub Packages

[XFactHD]

With FML updated to LWJGL 3.4.1, the Swing/TinyFD-based path of early error reporting works in the moved mod loading stages. However, when the ELS is enabled and the error handling therefore uses its infrastructure then the game segfaults in the Nvidia driver on my system when the ELS theme used by the ErrorDisplayWindow tries to upload textures.