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Is there a notion of holonomic D module which admits the six functor formalism in the world of twisted D modules?

Recall that twisted D modules on $X$ are well-defined for any $T$ torsor $\tilde{X}\to X$, see e.g. here. The twist is by a character $\chi$ of the torus. Of course the most important example of this is when $X=G/B$ is the flag variety of a semisimple algberaic group.

Pulcinella
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    You can think of twisted D-modules on X as ordinary D-modules on $\tilde{X}$ which are $\chi$-monodromic along the fibers. A twisted $D$-module is holonomic if and only if the corresponding $D$-module on $\tilde{X}$ is holonomic. In this way one should be able to deduce the correct functoriality behaviour. – Sam Gunningham Jan 30 '21 at 11:31

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