Since sqlite is local to your application, you can just bundle a newer version.
Speaking generally, if the Debian version is the way to go, the easiest way is often to grab the source package from sid and build it. It's literally just one command. Sometimes new dependencies will cause trouble, in which case some manual tinkering is required.
Here is an article from Julia Evans explaining it: https://jvns.ca/blog/2019/10/28/sqlite-is-really-easy-to-com...
Or if you are familiar with Docker, you can use a more recent Debian in a container and install sqlite inside it.