If you are expecting less than $25k in revenue (donations, grants, program service revenue, etc.) in each of your first three years, you can use the IRS's abbreviated process and get setup within a month (for the cost of setting up a corporation with your state government). If that exemption doesn't apply, it can take the IRS over a year to approve your application for tax exempt status. There are also significant compliance costs that can be burdensome for a small organization.

The TLF is a big dog for big dog projects, and I was just using them as an example of the structure. The Apache Foundation has their own flavor of governance, as does Numfocus (which sponsors a bunch of scientific computing projects). I'd expect that this move will probably trigger the creation of some "mobile app developer collective" organizations that specialize in this kind of thing, kind of like a "digital makerspace".

Could one sign over stewardship to the FSF? They're non-profit I think.

If you like to have an organizationalnumber, you need to apply to the tax authority. If you do business activity and like a local name protection you need to apply to bolagsverket. Depending on the size of the app these steps might be helpful. I don't think our local chapter of FSF, has done any of the registrations just as an example. They run local conferences and other simular works.