[pickers] Add satisfies casting to slotProps

[LukasTy]

Reopen #7859

[mui-bot]

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These are the results for the performance tests:

Test case	Unit	Min	Max	Median	Mean	σ
Filter 100k rows	ms	508.4	992.7	855.5	760	202.682
Sort 100k rows	ms	696.5	1,061.6	903.8	912.78	122.116
Select 100k rows	ms	214.5	402	316.3	295.04	69.966
Deselect 100k rows	ms	140.8	302.4	244.8	237.02	52.816

Generated by 🚫 dangerJS against 53b6746

[LukasTy]

We are getting errors because ast-types is unaware of the satisfies operator: benjamn/ast-types#935
This blocks us from using satisfies until ast-types updates it on their end, or monorepo bumps react-docgen, which no longer depends on ast-types and hopefully then the mentioned operator would finally be supported on all the chains.