Goodwill and Other Intangible Assets - Other Intangible Assets (Details) - USD ($) $ in Thousands |
Mar. 31, 2025 |
Sep. 30, 2024 |
|---|---|---|
| Other Intangible Assets [Abstract] | ||
| Carrying Amount | $ 220,796 | $ 581,691 |
| Accumulated Amortization | (134,021) | (455,665) |
| Net | 86,775 | 126,026 |
| Definite-lived trade names | ||
| Other Intangible Assets [Abstract] | ||
| Carrying Amount | 25,662 | 151,598 |
| Accumulated Amortization | (20,179) | (127,829) |
| Net | 5,483 | 23,769 |
| Customer relationships | ||
| Other Intangible Assets [Abstract] | ||
| Carrying Amount | 148,514 | 380,387 |
| Accumulated Amortization | (100,317) | (311,621) |
| Net | 48,197 | 68,766 |
| Copyrights/patents/other | ||
| Other Intangible Assets [Abstract] | ||
| Carrying Amount | 16,080 | 19,166 |
| Accumulated Amortization | (13,525) | (16,215) |
| Net | 2,555 | 2,951 |
| Indefinite-lived trade names | ||
| Other Intangible Assets [Abstract] | ||
| Carrying Amount | 30,540 | 30,540 |
| Accumulated Amortization | 0 | 0 |
| Net | $ 30,540 | $ 30,540 |