beanstalkd might be what you are looking for. It's ancient but solid af. I know of systems still running today that use it. For something more modern, check out Nats—and if you are using Go, you can embed the server in your executable.
I really like NATS, but it's worth noting that it's only really "the SQLite of queues" in the context of their Go client, which can embed a NATS server into an application.
Otherwise I would really say it is more like the Postgres of queues (still great, but potentially not what OP is looking for)
I’m sure there are better solutions on paper and for performance under common workloads. But if SQLite is good enough for your use case, it’s good enough for your use case.
Literally, the sqlite of queues.