- context diagram for an overview
  - uml sequence diagram for a more detailed view of interesting parts
  - entity relatioship model for databases

Petri nets have formal semantics easy enough to grasp (firing rule) and provide enough optical cues to make them readable at a glance.

With a little practice, nets can be visually appealing, which helps in presentations and publications. I use Inkscape as a drawing tool.

[0]: https://brandur.org/postgres-reads

Personally I prefer typing to drag-and-drop so I use https://www.gleek.io/

Check templates and turials, or ask me if you like to know more ;-)

But I've used Microsoft Visio in the past and it's a really nice solution (this was 3 years ago, so it might be better/worse now).

Component diagrams and deployment diagrams for the general overview, architecture and operations-wise.

Communication diagrams for some workflows.

Sequence diagrams to show how operations are executed.

For onboarding, sometimes a class diagram or two.

- diagram for high level

- diagram for small complex things

- comment on code as necessary

- write good enough documentation that is enough to onboard people to the project structure

- write decent commit messages