Are the Pokémon Sword and Shield expansion version exclusive?

To the first part, yes, according to https://ec.nintendo.com/AU/en/bundles/70070000009664 you need to buy the shield and sword expansion passes separately and are only usable with their respective versions.

As far as owning for example pokemon sword expansion, and your friend also using sword, that has not been definiteively answered, however, you can transfer pokemon caught on the expansion islands to games / players who do not own the expansion.

The official Pokémon website states that you have to purchase the version that matches you game version so you have to buy one for sword and one for shield. You get both expansions in the pass.

This Nintendo support answer says all DLC are available to profiles on the same console but the question was about Zelda. Howerver, having tried it myself I can confirm the expansion pass is available for all the profiles on the console.

As for the first part, yes, cause they're technically different games.

The second part, the expansion pack is available to profiles that are on the same console.

Other people have brought up some other sources before the expansion released, but now that they have actually released, I thought it would be worth to add my own experiences too to confirm them.

For the first part, I own both Sword and Shield. I bought the expansion for Sword (as it is the main one I play) as soon as it was possible to be bought. When the expansion actually released, it was playable on sword but not on shield until I bought the expansion for shield as well.

For the second part, any of my profiles can use the expansion (which I do find odd tbh). I have tested with all 3 profiles that are currently on my switch for both games.