It's not Dark Souls like at all. It's beat em up with classic Tomb Raider platforming and crap-ton of bugs and jank.
Dark Souls is an RPG with metroidvania-like level design.
That's rather misleading. Severance isn't a "beat em up" and you can't platform as if it's Tomb Raider: there are short jumps to make but no climbing and limited exploration and puzzling.
It is close to Demons Souls in the sense of it being a realistic-ish fantasy combat slasher. Souls series isn't famous for being an RPG or metroidvania, it's famous for its punishing, tactical combat that you have to take seriously (ie not a "beat em up" or typical RPG slash em up). In that sense it owes plenty to Severance, which is built around the skill-based melee combat.
Saying "It's not Dark Souls like at all" seems to me to be deliberately misconstruing how these games feel to play.
It most certainly is a beat em up - Dark Souls combat doesn't play like a fighting game, Severance does. Dark Souls isn't a slasher since you can use magic or bows legitimately
and make your own fighting style. And Dark Souls most certainly is famous for being RPG (see top RPG-s list of RPG Codex) and metroidvania (Yahtzee compares Dark Souls 1 to Castlevania: Symphony of the Night). It is a spiritual successor to From Software's King's Field series, after all.
Punishing tactical combat is present in plenty of Japanese beat em ups from the same period as Severance, titles such as Devil May Cry and Onimusha, and Souls reminds me more of Onimusha than Severance. Severance got more complex combat system which reminds me more of Soul Calibur series than Soulsborne series, only thing it shares with Soulsborne is perspective and stamina system, and stamina system is used differently in both games.