For the most part I am fine with Safari, but I also can't say there is any browser that I actually like using. I feel like one of the biggest problems is, well what are the alternatives? I use Firefox on my PC but since that is primarily for gaming I don't really need the interconnectivity. On my Mac, iPhone, and iPad the way everything works together is just way too valuable. I wish it's memory didnt just keep inchi…
I use KDE connect to get this functionality on Firefox/Chromium: https://kdeconnect.kde.org/
I'm sure you've probably had your ear talked-off hearing about this from an ex-Continuity user, so I really have little else to add. My laptop, desktop, phone and tablet all talk on the same network, and can send files and URLs over WiFi direct with a right-click context menu. After I started using Syncthing I never looked back at OneDrive or iCloud with a sense of regret. Synced media control via MPRIS, remote battery reporting and notification sync are the cherries on top. I call it, "The Freecosystem". You're all invited.