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Stock-Based Compensation - Narrative (Details) - USD ($) | 12 Months Ended
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Oct. 03, 2025 | Sep. 27, 2024 | Sep. 29, 2023
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Common stock, capital shares reserved for future issuance | 15,900,000 |  |
Vesting of stock-awards in connection with the transaction | $ 13,000,000 |  |
Compensation expense | 21,000,000 | $ 18,000,000 | $ 3,000,000
Income tax benefits recognized from stock-based compensation | 3,000,000 | 0 | 0
RSUs |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Unrecognized compensation expense | $ 27,000,000 |  |
Share-based compensation, weighted average period | 2 years |  |
Vested fair value | $ 1,000,000 | 0 | 0
RSUs | CMS |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Awards granted in the period (in shares) | 342,741 |  |
RSUs | Jacobs Solutions Inc. |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Non-vested awards outstanding (in shares) | 65,182 |  |
RSUs | Tranche One |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting rights, percentage | 50.00% |  |
Award vesting period | 2 years |  |
RSUs | Tranche Two |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting rights, percentage | 33.00% |  |
Award vesting period | 3 years |  |
RSUs | Tranche Three |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting rights, percentage | 25.00% |  |
Award vesting period | 4 years |  |
RSUs | Share-Based Compensation Award, Subject To Cliff Vesting |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting period | 3 years |  |
Stock Options |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting period | 3 years |  |
Performance Shares, Including Two-Year Market Condition |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Unrecognized compensation expense | $ 10,000,000 |  |
Share-based compensation, weighted average period | 2 years |  |
Employee Stock |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Common stock, capital shares reserved for future issuance | 2,500,000 |  |
Proceeds from stock plans | $ 3,000,000 |  |
Share-based compensation arrangement by share-based payment award, shares issued in period (in shares) | 100,000 |  |
Sale of stock, price per share (in dollars per share) | $ 22.75 |  |
Employee Stock | Employee Stock Purchase Plan |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Share-based compensation arrangement by share-based payment award, discount percentage | 5.00% |  |
Time Vested Class B Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting rights, percentage | 20.00% |  |
Award vesting period | 5 years |  |
Class B Units |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Unrecognized compensation expense | $ 0 |  |
Compensation expense |  | 18,000,000 | 3,000,000
Income tax benefits recognized from stock-based compensation | $ 0 | $ 0 | $ 0
Performance Stock Options | Minimum |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting period | 1 year |  |
Performance Stock Options | Maximum |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items] |  |  |
Award vesting period | 3 years |  |

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