I've always viewed Soulsbourne games as a 'modern' take on the Castlevania format;

• Exploring gothic settings with linear a linear destination but multiple routes/approaches
• Weapons with limited movesets but with additional items/spells to give you more options
• Respawning enemies with checkpoints to act as 'safe spaces'.
• Usually themed around ending the cycle of evil/darkness/blood
• Loads of secret / hidden areas with bonus lore / items

I guess the biggest difference is the characters and plot - Castlevania games usually have voiced protagonists with clear goals/aims, and obviously Dracula in some capacity.

LoS should have gone down the DS route rather than the DMC route imo. Castlevania has never been about flashy combos and momentum, to me it's always been about playing around with builds and finding the optimum way through levels.