Don't place docker containers or container /config files in a mergerfs pool.
A more nuanced response.
As the error suggests that software uses sqlite. sqlite3 has the ability to use mmap as a way to interact with backing files or regular read/write IO. Most software don't fail back to the latter if the former fails. The reason the former fails here is because you've setup mergerfs to use FUSE direct io mode which unfortunately doesn't support mmap on Linux. If you enabled page caching it would work fine. Theoretically I could try to be smart when files are opened/created and try to check if they are sqlite3 files and just enable page caching even if otherwise it is turned off. Probably wouldn't be a 100% though.
Ideally the offending software would correct this, IMO, poor behavior. Catch the error and fallback to regular IO. However, I've yet to see a project do this.
Further of this are in the mergerfs docs.
That said... I use a dedicated device and filesystem for all of my container's persistent storage as I didn't want it competing with my spinning rust and increasing their latency. Most software don't handle high latency well.