Can’t we just put the local SQLite file on a shared network folder?

This is the one shortcut that genuinely doesn’t work reliably. SQLite is excellent for local, single-user workflows, but it is not designed for concurrent multi-user writes over a network share — file-locking behaviour over SMB/NAS leads to errors, lost changes, or a corrupted file.
It’s a known limitation of network filesystem semantics, not something Project Manager can work around.
For real teamwork, use a database server (MySQL or MariaDB) — which is what this guide sets up.