Tuta and Proton, which are both commonly recommended, have not released their back-end code (read about it here and here). Proton doesn’t seem interested in open sourcing their code, and Tuta has claimed they’re aiming to do it in the future (the claim was made years ago and nothing has happened yet). They also both claim to be open source in their marketing.
Is there any alternative that is fully FOSS?
Posteo is mostly just a deployment of RoundCube.
Mind you, I do assume they have deployment scripts and code for handling payments and such, which aren’t open-source.
I also have to say, though, a hosted service using open-source is *nice*, because they will hopeful contribute back to that, but it’s not much beyond that.
You cannot know, whether they actually run the software that they publish in their repository, so auditing the open-source code hardly tells you anything about the trustworthiness of the actual service.