That’s pebble tiles. Like in a shower. I wouldn’t recommend.

Your architect had to indicate the different subfloor materials and depths. But that means you have to choose materials up front, before the home is designed, so that all the math is right.

If you were using something closer to 3/4" thick, you probably wouldn't have to worry. Why not? Because a tiled floor, once installed = 3/4" tall. A solid 3/4" hardwood = 3/4" tall. Or a 12mm (1/2") laminate + 6mm cork underlay (1/4") = 3/4" high. Or a 15mm laminate + 3mm cork underlay = 18mm = 3/4" (or very close to).

Sadly the LVP is the stuff that is SUPER hard to deal with when trying to 'match' a floor height. And to be clear, LVP does NOT like underlayment unless it is plywood or OSB. Soft squishy stuff is NOT allowed with LVP.

Oh...and LVP HATES HEAT! Yes. Hates. It. With. A. Passion. LVP (vinyl....like mum N dad's records) will shrink and warp and do all kinds of neat things in the presence of heat. Dry heat (from a wood burning oven...or even gas fireplace) is the worst. It shrinks more than you would ever know.

Just a few thoughts. Personally I prefer a thick, high-end laminate + cork underlayment as a floor. It is so much easier to live with...and it couldn't care less about heat or sunlight.

You'll need to build your hearth to the R value required by the stove. Select your stove first.

https://www.chimneysweeponline.com/horvalue.htm

Don't have a wood stove. Build a fireplace. Gas or real.deal . : )

The only way I know to do this is to recess the sub flooring into the floor framing to make room for the materials that meet the above mentioned heat resistance. That's the way flush fireplace hearths have been installed for centuries.

Many wood stoves have a shelf that helps protect the floor from ashes and direct exposure to radiant heat from the firebox. The stove you posted is an odd one. Choose the stove first and read the installation instructions.

There are tons of choices for wood stoves so go to a good fireplace shop and choose a stove and install properly for the stove you choose and the code where you live how it looks is secondary . The pic you show would not pass inspection where I live since you would still need fireproofing behind the stove too.

The stove in the picture is a Woodstock Keystone which requires a rear clearance to combustibles of 14.5" with the optional heat shield. If you like that stove, check out the Woodstock stoves, they are one of the best and most efficient in the industry. You won't find them at your local fireplace shop as they are semi custom, factory direct only.

We have a wood stove with a slab of soapstone underneath it and solid wood flooring butting up right against the soapstone. Same level, no toe-stubbing, have never had any issues with the floors.

Another alternative would be to use a sloped threshold (ramp) that is made for transitioning different height materials and the toe stubbing issue goes away.

Does the area have wood or concrete subfloor? If concrete, the easiest option would be to install the LVT, then float the stove area with a concrete topping product like Ardex PC-T. If it's wood you'll need to consider fire resistance. Being in south Florida, I have no experience on that topic.