[noun] + を契機に、[sentence] [noun] + を契機にして、[sentence] [noun] + を契機として、[sentence] [verb (plain)] + の / こと + を契機に、[sentence]
を契機に goes after a noun for an event and makes it the turning point for what follows: "prompted by", "since". The event is a weighty one – an illness, a disaster, a marriage, a law – and the second half is a lasting change. A verb clause takes の or こと first. It is formal and mostly written.
The change can be one somebody decided or one that simply happened in society: nobody chose for remote work to spread.
All three mark a turning point. をきっかけに is the everyday one and takes small events as readily as big ones. をき機に treats the event as an occasion someone chose for a change. を契機に is the most formal and the one for history, policy and society.
を契機にして and を契機として mean the same as を契機に; として sounds the most formal.