Let’s tear this apart.

Length overall: 165.8 m Beam: 23.0 m Draft: 8.6 m

Not a nautical engineer, but those seem to be comparable to known military craft. So that’s probably a decent envelope for a sub carrying ordinance and full crew. So, lots of free space for a pleasure craft.

Range: approx. 15.000 km

To pump these numbers, that’s likely surface cruising at some optimal speed. We can safely say this isn’t a nuclear sub, since that would be something to boast: your “range” is really “how much food do you have?” since that runs out first.

Submerged duration: approx. 4 weeks

This one’s tricky. There are ways to generate O2 without electricity. But the rest of your environmental controls like heat, light, plumbing, cooking, etc. draw power. So we can assume a pretty beefy battery bank on this boat, but not excessively so, in order to stretch into that 4 week range. But that’s nothing revolutionary for subs - Electric subs go back to 1888, with diesel/electric hybrids coming along after that.

Depth: approx. 250 m

Totally plausible and shallower than military craft. But maybe not with the viewing windows in the illustration.

It even has a pool inside it!

A moon pool or a regular one? Either way, that’s extravagant. But it looks like a moon pool wouldn’t work below 50m or so.