It seems that blockpack functionality was completely removed in version 1.3.X. Is this intentional, and the way that this mod will be moving forwards in the future? Because if so, I don't think there's really any reason to use it.

Discussed in discord, response was

I'll reimplement the AARP data-driven parts of the mod in 1.4.x, that's why I'm still holding two branches on github, but right now I'm going about a precompiled data driven approach with python scripts for better load times for the large mass of the blocks, because I added 1000 more blocks on top of the already 1,200 that were already there and my crappy laptop was at it's knees at load times. sorry for giving you a bad time, I should of made it more obvious on the page where it says that 1.3 and 1.2 aren't compatible, but when I drop 1.4.x all the previous blocks should be able to load

So I'll close this issue for now!

This is fixed completely in 1.4.1, with automatically replacing blocks that were in 1.2 to the 1.3 version.
https://github.com/matthewperiut/Chisel-Fabric/releases/tag/v1.4.1
AARP will be implemented with a new folder formatting later in 1.5.x, but specifically 1.4.x is for parity since it relies on a quite old version of AARP. So I'll let it be for a while then bring in a data-driven way to add blocks.