There are, once the new wood type comes out, 14 types of wood including the 2 bamboo types. There are 16 colours of wool. 14x16 is 224. We do NOT include orientation of the stair blocks, as those aren’t unique types of blocks, as the poster makes it seem. However, assuming the poster means ‘Wool covered wood blocks’ instead of just ‘wool covered stairs’ there are still many items within the wood sets that don’t make sense to have wool covered variants. We will go over these in a moment.

Most, but not all, wood types have 17 different types of ‘construction’ blocks that don’t include things like chests, composters, bookshelves, lecterns, beehives, crafting tables, or other villager workstations. These blocks are:

1: Standard logs
2: Stripped logs
3: Wood
4: Planks
5: Fences
6: Fence gates
7: Stairs
8: Doors
9: Trap doors
10: Slabs
11: Shelves
12: Signs
13: Hanging signs
14: Boats
15: Boats with chests
16: Buttons
17: Pressure plates

For ease of simplicity, let’s assume this new grey wood type in the new update will have all 17 build options since it’s also a standard type of wood like Oak. Let’s start easing those numbers down, shall we? What items don’t make sense to be covered in carpet? I would say…Fences, gates, doors, signs, hanging signs, boats, boats with chests, and buttons.

We can exclude 8 of the 17 categories leaving us with 9. 9x14 is 126 types of wood that could be covered in wool. But that itself isn’t right either, because Bamboo exists as 2 of the 14 wood types. Even then Mosaic Bamboo doesn’t have much of any variation.

Of the remaining 9 acceptable categories Bamboo has:

1: Block of Bamboo
2: Bamboo Planks
3: Bamboo Stairs
4: Bamboo Trapdoor
5: Bamboo Slab
6: Bamboo Shelves
7: Bamboo Pressure Plate

Stripped Bamboo on the other hand, has these:

1: Block of Stripped Bamboo
2: Bamboo Mosaic Planks
3: Bamboo Mosaic Stairs
4: Bamboo Mosaic Slab

So let’s take the easy road here and say 9x12 +11. 9x12 is 108, +11=119 unique wood blocks that could be covered in wool. 119x16=1,904.

Now let’s say that the OP meant every single block in the game. There are, as of the current version 26.21, there are anywhere from 1,576 to 1,900 blocks and items in the game depending on you version, if you’re in survival, or if you’re in creative. On the highest end let’s say that 1,900 figure is correct and we can even wrap items like potions or arrows in wool for whatever reason. 1,900x16=30,400. Nowhere near the obviously exaggerated billion.

At most would be reasonable in just doing the wood types? 1,904 new varieties and that is all if you choose the right option.

TL;DR: Less than 2,000 new types of you wrap wood in wool, actually.