Are there any databases of templates for common bioinformatic file formats?
You mention Biopython, which contains tests: https://github.com/biopython/biopython/tree/master/Tests.

Some of the tests consist in reading files present in the folders listed in the above link. These files could be a starting point for a database of test files. Whenever one comes across a test case not covered with these files, one could construct a new test file and contribute it to Biopython, along with a test, or at least file an issue: https://github.com/biopython/biopython/issues.

That would be a way to contribute to Biopython while constituting a database of test files.