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Other Assets - Schedule of Other Assets (Details) - USD ($) $ in Millions | Dec. 31, 2023 | Jan. 01, 2023 | Jan. 02, 2022
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Other Assets [Line Items] |  |  |
Life insurance cash surrender value | $ 230.3 | $ 194.3 |
Intangibles, net of accumulated amortization | 137.7 | 158.7 |
Noncurrent restricted cash | 8.0 | 8.6 | $ 6.6
Workers' compensation receivable | 11.7 | 12.1 |
Other | 15.7 | 15.8 |
Total other assets, including held-for-sale | 416.5 |  |
Total other assets | 411.1 | 403.2 |
Equity securities, FV-NI and without readily determinable fair value | 6.4 | 6.4 |
Intangible assets, accumulated amortization | 64.1 | 44.9 |
PersolKelly Pte. Ltd. |  |  |
Other Assets [Line Items] |  |  |
Equity securities, FV-NI and without readily determinable fair value | 6.4 |  |
Disposal Group, Held-for-Sale, Not Discontinued Operations | European Staffing Operations |  |  |
Other Assets [Line Items] |  |  |
Total other assets | 5.4 |  |
Other Assets |  |  |
Other Assets [Line Items] |  |  |
Intangible assets, accumulated amortization | 76.6 | 55.5 |
Long Term Hosted Software, net of accumulated amortization |  |  |
Other Assets [Line Items] |  |  |
Intangibles, net of accumulated amortization | 13.1 | 13.7 |
Long Term Hosted Software, net of accumulated amortization | Other Assets |  |  |
Other Assets [Line Items] |  |  |
Intangible assets, accumulated amortization | $ 14.2 | $ 7.3 |

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