It is somewhat of a problem: the development team is very small, they don't take outside contributions (so nobody outside the core team really builds up expertise over time), and the vast majority of tests are proprietary. I hope they have a contingency plan just in case (some sort of a dead man's switch that publishes the test suite under a permissible license) as it would probably be quite difficult for others to maintain the same quality without those tests, or re-implement them in a reasonable time frame.
But that equally applies to getting critical bug fixes for your particular usage scenario of SQLite. It's not just about the viability as a storage format.
For the latter, because the stored data has such a simple format and the implementation has so few dependencies, I expect it will be very easy to get your data out for a long time to come. It's going to be tougher if you have business logic in views or other SQL expressions, of course, and if you rely on SQLite's particular approach to data types (as in “values have types“, but not much more).
https://www.sqlite.org/locrsf.html
https://www.sqlite.org/lts.html