I would use the underlayment required by the LVP manufacturer as their product warranty will only be in effect with the underlayment they require.

There is no such thing as a dry sauna. Even with an IR cabin you can be dripping sweat on the floor. With a sauna you throw water on the stones to create steam, you typically sweat much more than with an IR cabin, and with IR cabins and saunas you need to wash the benches which results in a good bit of water on the floor.

Saunas and supporting areas are generally considered wet areas. You shower, go to sauna, rinse off in the shower, go outside to cool down, rest, repeat.

So for an interior space like this tile flooring built like a WC is often the best option.

Also, attics can be poor locations if they don't allow easy wet access to outside. Something to think about before investing a lot of money.

More:

https://localmile.org/trumpkins-notes-on-building-a-sauna/

https://saunologia.fi/in-english/

Does wine cellar look completed no refrigeration.

Saunas and supporting areas are wet spaces. You need to be able to shower > sauna > shower > go outside to cool down or jump in a cold plunge > rest > repeat.

That area does not look like it would be a good location for a sauna (and the tile looks like it'd be slippery when wet).

More:

https://localmile.org/trumpkins-intro-to-sauna/

https://saunologia.fi/in-english/

What are you thinking for the sauna?

Your move to a white sink sounds like a useful simplification. With the sauna and tub already providing the room’s character, I’d let those be the features and add personality through something easy to change—art, towels or a small accessory.

Before buying the remaining pieces, have your designer check the measured layout against the exact sauna and tub specifications, including door movement, required clearances and access for cleaning. In a compact room, comfortable use deserves as much attention as fitting everything in.

Which sauna model have you selected, and could you share the scaled sketch you mentioned? That would help focus suggestions on the space you actually have.

I love the direction you're going with this! The light oak, matte black, and thin gold accents could make such a beautiful combination, especially with the sauna.

For the fun feature, I'd consider a small section of vertical wood-look slat tile or a textured accent wall. Something that adds personality through texture rather than introducing another bold color.

We did a zen bathroom at our old house and here's what we put on our list, some we used, some we didn't

Mirror https://link.amazon/B0aFrDzSE

Slats https://link.amazon/B00fIOCsC

Teek Stool https://link.amazon/B0fatHw4t