Goodwill and Intangible Assets - Changes in Goodwill (Details) $ in Thousands	3 Months Ended
	Dec. 31, 2021 USD ($)
Goodwill [Roll Forward]
Goodwill, beginning	$ 292,243
Goodwill attributable to preliminary purchase price adjustments and acquisitions during the three months ended December 31,2021	57,354
Goodwill, ending	349,597
Merchant Services
Goodwill [Roll Forward]
Goodwill, beginning	119,086
Goodwill attributable to preliminary purchase price adjustments and acquisitions during the three months ended December 31,2021	0
Goodwill, ending	119,086
Proprietary Software and Payments
Goodwill [Roll Forward]
Goodwill, beginning	173,157
Goodwill attributable to preliminary purchase price adjustments and acquisitions during the three months ended December 31,2021	57,354
Goodwill, ending	230,511
Other
Goodwill [Roll Forward]
Goodwill, beginning	0
Goodwill attributable to preliminary purchase price adjustments and acquisitions during the three months ended December 31,2021	0
Goodwill, ending	$ 0