Yes there are elements of older From Software games in the SB games and that is because their philosophy of game design has never changed. From Software didn't really have any clout in the industry during their earlier years and have admittedly stated that they were a studio know for making pretty "shitty games".
With all this said, they kept creating what they actually wanted to create. It seems like From Software is a dev that has creative freedom and are not bound like some other studios that only make 1 type of game/series of games. Their titles ranged from survival horror games, to mech shooters and first person dungeon crawling RPG's.
Miyazaki internally at the studio was someone that wanted to be involved in everything and quickly became someone they looked up to due to his ability to make quick decision in projects (a problem a lot of directors/decision makers have). I don't think the industry talked a lot about Miyazaki when he directed and released Armored Core 4 in 2006. It wasn't until Demon's Souls and particularly Dark Souls that the average gamer and the industry started praising him. Why is that? Because the game was something different and strayed far away from the norm in the industry both in the difficulty department, risk & reward of loosing all your progress after one mistake and the indirect story telling.
DeS and DS came out at a time where the majority of AAA games held your hand and didn't challenge you at all. Creating a challenge to overcome has been one of their core pillars of game design even in their older titles. With the help of bigger publishers like Sony and Bandai they were able to put out games with a bigger budget and greater outreach so more people could experience them.
Demon's Souls became much beloved after a while and Dark Souls even more so. Who was behind the game in the director seat at that time? Hidetaka Miyazaki. Dark Souls showed the industry that it is ok for AAA games to be very challenging like the old days of NES and SNES again. Years to follow there have been countless games ramping up the difficulty and admitting they were very inspired by From Software's philosophy of game design which really had always been the same.
What Miyazaki brought to the table is very simple. He was in charge of the games that took the company from "Who are these guys?" to "Oh my god From Software is announcing a new game". He seems to be someone that knows how to execute games during their development and has proved that with each project he has been involved with during the past decade. Even if their ways of creating games hasn't changed much, nobody before him managed to have a significant impact on the industry during the lifetime of that company.
Here are some of the sources I looked at: [HM Wiki]{https://en.wikipedia.org/wiki/Hidetaka_Miyazaki} | [FS Wiki]{https://en.wikipedia.org/wiki/FromSoftware} | [GI Interview] {https://www.youtube.com/watch?v=r6F5flVQRus&t=40s}