Can different appearance types have different calendar formats?

Yes. Each appearance type (and each event type) can have its own calendar format, on top of the default you set under Settings → Calendar format.

1. Click + Custom override on the Court dates or Events tab.
2. Choose the appearance types (or events) it applies to. Everything you haven’t named keeps your default format.
3. Edit and save. An override is a complete format in its own right: it opens as a copy of what you already write, and the preview switches to one of your own entries of that kind.

From the next entry Acquit writes, matters of the chosen type use the override and everything else stays on the default.

Note: Each tab allows up to five overrides; the first match wins when two name the same type, and an override with nothing chosen does nothing until you pick something.