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Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2023 | Sep. 30, 2022 | Sep. 30, 2021
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 333,205 | $ 284,499 |
Finite-lived intangible assets, accumulated amortization | (106,296) | (88,622) |
Finite-lived intangible assets, carrying value | 226,909 | 195,877 |
Total identifiable intangible assets, cost | 333,248 | 284,541 |
Total identifiable intangible assets, carrying value | $ 226,952 | 195,919 |
Estimated Useful Life | 3 years |  |
Amortization expense of intangible assets | $ 20,539 | 17,892 | $ 15,830
Trademarks |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Indefinite-lived intangible assets | 43 | 42 |
Customer relationships |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | 310,501 | 268,301 |
Finite-lived intangible assets, accumulated amortization | (98,182) | (80,681) |
Finite-lived intangible assets, carrying value | $ 212,319 | $ 187,620 |
Customer relationships | Minimum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 9 years | 10 years |
Customer relationships | Maximum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 25 years | 25 years |
Non-compete agreements |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 1,300 | $ 1,190 |
Finite-lived intangible assets, accumulated amortization | (1,059) | (705) |
Finite-lived intangible assets, carrying value | $ 241 | $ 485 |
Non-compete agreements | Minimum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 3 years | 3 years |
Non-compete agreements | Maximum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 6 years | 6 years |
Website and brand development costs |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 44 | $ 268 |
Finite-lived intangible assets, accumulated amortization | (37) | (159) |
Finite-lived intangible assets, carrying value | $ 7 | $ 109 |
Website and brand development costs | Minimum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 3 years | 3 years |
Website and brand development costs | Maximum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 4 years | 4 years |
Trade names |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 6,531 | $ 7,771 |
Finite-lived intangible assets, accumulated amortization | (3,690) | (4,203) |
Finite-lived intangible assets, carrying value | $ 2,841 | $ 3,568 |
Trade names | Minimum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 3 years | 3 years |
Trade names | Maximum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life | 7 years | 7 years |
Residual buyouts |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 14,220 | $ 6,169 |
Finite-lived intangible assets, accumulated amortization | (3,111) | (2,141) |
Finite-lived intangible assets, carrying value | $ 11,109 | $ 4,028 |
Estimated Useful Life | 8 years |  |
Residual buyouts | Maximum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life |  | 8 years |
Referral and exclusivity agreements |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Finite-lived intangible assets, cost | $ 609 | $ 800 |
Finite-lived intangible assets, accumulated amortization | (217) | (733) |
Finite-lived intangible assets, carrying value | $ 392 | $ 67 |
Estimated Useful Life | 5 years |  |
Referral and exclusivity agreements | Minimum |  |  |
Finite-Lived Intangible Assets [Line Items] |  |  |
Estimated Useful Life |  | 5 years |

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