Shellite and Twinite can be melted down in a Tinker's smeltery, but cannot be dispensed back into ingot form or coin or block, etc.

Dragonsteel and Soul-Infused work as expected.

This is version 2.0.2 for Minecraft 1.18.2

Would like to report, just started playing again recently and am using the 2.0.3 version for 1.18.2.

Shellite and Twinite still can't be dispensed from a Tinker smeltery like the other materials.