Tags

The mod adds its blocks to these vanilla tags, so anything that works with vanilla walls, slabs or buttons also works with them. It adds no tags of its own.

Tag	For	Blocks	Covers
#minecraft:buttons	block, item	33	All buttons
#minecraft:mineable/pickaxe	block	66	All stairs, slabs
#minecraft:pressure_plates	block	33	All pressure plates
#minecraft:slabs	block, item	32	All slabs except Terracotta Slab
#minecraft:stairs	block, item	32	All stairs except Terracotta Stairs
#minecraft:walls	block, item	33	All walls

Walls are not listed in #minecraft:mineable/pickaxe themselves: vanilla already includes the whole #minecraft:walls tag there, so terracotta walls are mined with a pickaxe too.

Plain terracotta stairs and slab

terracottathings:terracotta_stairs and terracottathings:terracotta_slab are missing from the stairs and slabs tags in the current version. They still work normally in the world, but recipes or mods that look for any stairs or slab by tag skip them. A datapack can add them:

// data/minecraft/tags/block/stairs.json (and the same under tags/item/)
{
  "values": ["terracottathings:terracotta_stairs"]
}

Do the same in slabs.json for terracottathings:terracotta_slab. Leave out "replace": true, so your file adds to the tag instead of replacing it.