As far as I’m aware, the only self hosted player character builder is the charactermancer in plutonium, the patreon-accessible Foundry VTT plugin made by the 5e.tools folks — but man. My kingdom for a dndbeyond alternative, something self hosted that can take open 5th edition content and allow my players to build and save their character sheets. I don’t suppose I’m just missing something already out there, or are there any projects I should be following?
Aurora is no longer maintained, but it still works just fine. It’s a Windows app, so not web-accessible or anything, but it’s free. It only contains the SRD content by default (probably for legal reasons), but there’s at least one publicly-accessible elements repository for it that you can find using your favorite search engine.