When Wikibase formats time values as HTML, it automatically shows the calendar model if needed (depending on the precision, date, and what the automatically guessed calendar model would be for that date). However, formatting times as wikitext or plain text only formats the time value itself. Lua modules can add the calendar model “manually”, but Wikibase’s logic deciding when to show the calendar model or not isn’t accessible to them.
=mw.wikibase.formatValue({snaktype = 'value', property = 'P569', datatype = 'time', datavalue = {type = 'time', value = {time = '+1879-03-14T00:00:00Z', timezone = 0, before = 0, after = 0, precision = 11, calendarmodel = 'http://www.wikidata.org/entity/Q1985727' }}}) <span>14 March 1879</span> =mw.wikibase.renderSnak({snaktype = 'value', property = 'P569', datatype = 'time', datavalue = {type = 'time', value = {time = '+1879-03-14T00:00:00Z', timezone = 0, before = 0, after = 0, precision = 11, calendarmodel = 'http://www.wikidata.org/entity/Q1985727' }}}) 14 March 1879