I don't have Apple devices to compare, but I think KDE Connect can closely replicate this, entirely locally. I wouldn't be surprised if Apple's "deep integrations" rely on cloud components that are privacy-violating by design (even if Apple promises not to look at the data flowing through their servers).
Unfortunately the integration is really quite weak with Apple. KDE Connect cannot remain active while the application is not in the foreground. It’s possibly a packaging issue but pairing from fedora is also quite flakey.
As absurd as this sounds windows -> iPhone via their phone link is actually almost as good as apples built in ecosystem to the point where I can make phone calls and send texts on my computer. It’s not quite as seamless especially the setup but that is a well done wizard and it mostly works.
KDE Connect with iOS, while useful, is terrible.
Most cross device stuff in the Apple world actually works via P2P Bluetooth and WiFi and functions without an internet connection or even a shared WiFi network. Mac and iDevice WiFi hardware is even designed with this in mind and is capable of maintaining P2P connections to other devices and a WiFi network simultaneously without rapidly switching between the two like many commodity WiFi cards have to.