`@mui/styled-engine@6.1.3` incompatible with `@mui/system@6.1.1`

[Janpot]

Steps to reproduce

Originally commented on #44105, but it's a different issue

Seeing issues in mui/toolpad#4257. @mui/styled-engine@6.1.3 is not compatible with @mui/system@6.1.1 even though the latter declares its dependency on @mui/styled-engine as ^6.1.1. Something similar is going on with @mui/utils. The result is that package managers may update transitive dependencies according to semver and break setups.

There's a workaround described in mui/toolpad#4257 that uses package manager resolutions.

Reproductions:

• reproduction for internal_processStyles in Stackblitz
• reproduction for @mui/utils/getReactNodeRef in Stackblitz

Looks like it's caused by a set of breaking changes to internal APIs:

• Offending PR [system] Pre-serialize & cache styles to improve performance #43412 that removes the internal_processStyles in @mui/styled-engine.
• Offending PR [core] Improve getReactElementRef() utils #43022 that removes @mui/utils/getReactNodeRef

Current behavior

No response

Expected behavior

No response

Context

No response

Your environment

npx @mui/envinfo

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  Output from `npx @mui/envinfo` goes here.

Search keywords: internal_processStyles

[aarongarciah]

Today we merged #44248 to bring @mui/utils/getReactNodeRef back. @mnajdova do you have an idea on how to fix the internal_processStyles case?

[github-actions]

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