Features:

• Advancements can be clicked and dragged to freely change their position
• Set a fixed order for the advancement tabs to sort into
• Adjust the window size of the advancements screen
• Add fancy backgrounds with random variation to the tiling blocks

Details:

• Edit Mode for rearranging advancements can be toggled in the config. Make sure not to disable it while the advancements screen is still open, or any changes won't be saved.
• While rearranging advancements, hold shift for position snapping
• To render a resizable window, the vanilla gui texture (at minecraft:textures/gui/advancements/window) is tiled using 9-slice scaling, with a configurable slice margin

Persistent data (advancement positions, fancy backgrounds) is stored per-instance at /minecraft/advancements_arranged.json An example such file, providing the vanilla advancement tabs with custom layouts and fancy backgrounds, can be found [here].

Likely not compatible with other mods which overhaul the advancements screen, as they tend to re-implement it with their own custom gui, whereas this works by modifying the vanilla gui directly.