I regularly switch between a MacBook for work, Linux desktop at work, Windows 10 home machine, iMac home machine, iPad, and iPhone, using at least two browsers on each (Chrome/Safari or Chrome/Edge) and often two Chrome profiles.

I use 1Password with the encrypted vault synced to Dropbox and it works wonderfully well. 1Password has native apps / browser extensions for all of those platforms (except Linux local app where they support and recommend using Wine).