Chrome and Edge are proprietary wrappers around Chromium (BSD license). Firefox and derivatives are FOSS (Mozilla Public License). Safari is built around WebKit (LGPL/BSD).
The problem, however, is governance. These projects are all too big for anyone to realistically fork and maintain independently. So in practice, they are under control of Google, Mozilla, and Apple — all of which have questionable priorities (especially Google).
All major browser engines are FOSS.
Chrome and Edge are proprietary wrappers around Chromium (BSD license). Firefox and derivatives are FOSS (Mozilla Public License). Safari is built around WebKit (LGPL/BSD).
The problem, however, is governance. These projects are all too big for anyone to realistically fork and maintain independently. So in practice, they are under control of Google, Mozilla, and Apple — all of which have questionable priorities (especially Google).