Migration Source YML File import date string into date and time field of content type
The migrate plugin that handles this is FormatDate.  It looks like you are missing the input and output date formats.  For date-only, you would do something like

process:
  field_date:
    plugin: format_date
    from_format: 'm/d/Y'
    to_format: 'Y-m-d'
    source: event_date


and for date+time, it would look something like

process:
  field_datetime:
    plugin: format_date
    from_format: 'm/d/Y H:i:s'
    to_format: 'Y-m-d\TH:i:s'
    source: event_time


When migrating into the core datetime/daterange fields, the to_format needs to be those strings (these were written to be generic, not just for those field types).  The from_format gets adjusted to your input source.  If you look at the references below, there is also a way to specify time zone.

That plugin is unit tested, so core doesn't provide any YAML example, but you may be able to glean samples from FormatDateTest.

References:


Added FormatDate migrate process plugin
https://www.drupal.org/project/drupal/issues/2820490
FormatDate migration process plugin now supports specifying of source and destination timezones
https://www.drupal.org/project/drupal/issues/2883892