Short answer
The useful part first.
Yes. In the launch AMA, the developer said Pax Autocratica lets you save anytime and anywhere, including during a roguelite expedition. The official Steam page also lists Steam Cloud support.
Can you save during an expedition?
Yes. The developer’s answer covers the roguelite expedition itself, so you do not have to finish an entire expedition merely to create a save. That statement is broader than an autosave-only checkpoint system.
What does Steam Cloud add?
Steam Cloud can synchronize supported save data between Steam installations. It is separate from the game’s ability to save mid-expedition: one creates progress data, while the other can copy supported data through Steam.
What Steam Cloud does not guarantee
A Cloud-support badge does not guarantee conflict-free recovery after every interrupted upload, offline session, or manual file change. When Steam presents a sync conflict, compare timestamps carefully before choosing a version.
Why there is no save-file path here
The official sources reviewed for this page do not publish a supported save-file location or manual restore procedure. We will not guess at a path that may change across builds or lead players to overwrite progress.