The style guide's entry for agonising explains that it is the British spelling of the word.

She was agonising over whether to accept the job offer, torn between opportunity and family.

Her agonisings over the decision lasted for days before she finally chose to move abroad.

Don't agonise over the decision; we'll support whatever you choose.

He agonises about whether to accept the job offer, staying awake most nights.

She agonised over the decision for days before finally calling him.

She watched agonisingly as the deadline approached, unable to finish her report.