Steve drove (Chief Operating Officer) Marco Landi and (chief technologist) Ellen Hancock out even before he became CEO. Bertrand Serlet (1997-2009) then Craig Federighi (2009-) ran the (variously named) OS team and Avie Tenivan was the tech lead, all former NeXT folks (which makes sense because Apple failed at 3 OS projects then shipped reskinned NeXTStep). Bud Tribble followed Steve to NeXT then back to Apple in various VP roles. George Crow and Jon Rubinstein did the same kind of loop working on hardware platforms at Apple-NeXT-Apple. Mitch Mandich became SVP of sales almost immediately after the acquisition. Etc.
The Objective-C Cocoa APIs are a straight descendant of the NeXTStep APIs, and many NeXT apps would run on OS X with a simple recompile. While there have been many additions since, and the main focus these days is on the Swift language, to the best of my knowledge, you can still take an Objective-C NeXT application and compile it on your ARMintosh and have it run with very few issues.
I was a Mac user from 1989, and I didn't like OS X much at the time. It felt like a completely new system, not an update to what I was used to. Sure, it was better in many technical ways, but it was also a lot more complicated. And it felt different. So there were was definitely a sense that it was really a Mac anymore.
Just about the only technical concession to the old Mac crowd that I can think of was the use of the old HFS+ file system, over NeXT's UNIX filesystem. And I think this was only because there was a transition period of several years where dual-booting was common, even necessary. So you could install OS X next to your old OS 9 system and boot either at your discretion without having to have several partitions. Mac OS9 is very dependent on some features in its FS, so this was the only way to allow a smooth transition. But other than that, OS X was and felt like a new, alien system, even though it did allow for compatibility with many applications.
Also, early versions of OS X (IIRC though 10.4) were perfectly happy to install and work on UFS, the installer would even help you do so.
From the user end, the problem with running OSX on UFS was that... a bunch of sloppy software broke on case-sensitive volumes. Famously, Adobe's entire suite wouldn't even install on case-sensitive volumes (see https://helpx.adobe.com/creative-suite/kb/error-case-sensiti... I think it's still unfixed to this day). This is probably also the reason why despite Apple finally getting a modern file system... APFS has and defaults to a case-insensitive mode in opposition to essentially every other modern FS.
Fun times!