Is it possible to transfer just an app's mysql/mariadb database info into a new installation of nextcloud?

I can’t say anything about the Deck app, but the relevant data for calendars is stored in these tables - some of those might have been introduced after Nextcloud 19 (your table prefix might be different from oc_):

oc_calendarchanges
oc_calendarobjects
oc_calendarobjects_props
oc_calendars
oc_calendarsubscriptions
oc_calendar_invitations
oc_calendar_reminders
oc_calendar_resources
oc_calendar_resources_md
oc_calendar_rooms
oc_calendar_rooms_md
oc_dav_cal_proxy
oc_dav_shares
oc_group_user

As calendardata is spread over several tables and also synchronization status and other information is stored along with the data, I think just directly importing these tables is quite error-prone.

If there are not to many users and calendars and as long as you have access to the database of the broken instance, you could also export the calendardata to *.ics files with calcardbackup and then import the *.ics files to the new instance.