Another ship that appeared in earlier episodes and the Short Trek "Children of Mars", we get our clearest look at this type of shuttlecraft as the taxi Picard takes to see Raffi in "Maps and Legends". This shuttle is also seen flying over Vashti in "Absolute Candor" and is a reuse of the Class C Starfleet shuttlecraft from Star Trek: Discovery.
As this shuttle is never seen used by Starfleet in Star Trek: Picard, we can infer from its deployment as a school bus in "Children of Mars" and as a taxi in "Maps and Legends" that this is old Starfleet tech repurposed for civilian use.
It's also possible the use of the Class C shuttlecraft in Star Trek: Picard is simply a cost saving measure by the producers and is intended to be a totally different design that just happens to be identical to the shuttle from Star Trek: Discovery. Star Trek is no stranger to reusing existing ship models (physical and CGI) over its different eras, but it is a bit strange that a 160 year old shuttlecraft would still be in operation.