I'm currently playing through Harmonious Engineering 3 with a couple of extra mods installed. Today when I was playing, I suddenly realized I couldn't mine, at all. It's been a little while since the last time I was mining as I'd just been crafting components for machines so I've no idea when it started.  However I can't find a solution. It's like the game doesn't recognize any pickaxe as a pickaxe? Like a drill item worked, but nothing else has been able to mine stone. Dirt is fine, wood is fine, but anything meant for pickaxes is like mining with a open hand, it doesn't even drop. Please let me know how to fix this.

There can be numerous issues here as it could be one of the mods in the pack or the extra ones you provided. You can test if its Forge by creating a duplicate of the world and loading it with no mods and attempt to break something. If it's one of the mods, you'll need to narrow it down yourself. If one in the pack, it's best to report it to the pack creator and the mod author. If not, report it to the mod author.

Judging by the description, it seems like a datapack in one of the mods replaced the tag entries when mining with a pickaxe.