How much is usually deposited in a Mars regional dust storm? Is there any indication of how much dust is deposited, especially in areas that are not open where wind might produce a cleaning event?
Philip R. Christensen wrote an article back in 1986 called Regional dust deposits on Mars: Physical properties, age, and history. The abstract says

Dust deposited during global storms is subsequently removed only from dark regions, resulting in a net accumulation in the low‐inertia, bright regions. The thickness of these current dust deposits is 0.1–2 m.

This rather rough approximate for global storms seems to be a upper boundary, because e.g. Bruce Cantor states in the abstract of the article MOC observations of the 2001 Mars planet-encircling dust storm, the dust storms observed by the two rovers do deposit significantly less material (but can still cover solar cells):

The storm caused substantial regional albedo changes (darkening and brightening) as a result of the redistribution (removal and deposition) of a thin veneer of surface dust at least 0.1–11.1 μm thick.

However, the abstract also says that local storm events might significantly redistribute material:

The redistribution of dust by large annual regional storms might help explain the long period (∼30 years) between the largest planet-encircling dust storms events.

Both articles are paywalled, so I could not dig deeper here, so let us explore a bit a very local phenomenon, namely the dust devil. Dust devils have been frequently observed on Mars.
S.M. Metzger, Matt R. Balme et al. give an estimate of mass transport per dust devil in their article In-Situ Measurements of Particle Load and Transport in Dust Devils:

We find that dust devils [...]  can  loft  about  1  kg  of  PM10  material  to  heights  of  several  hundred  meters over their lifetime. Furthermore, applying the 5-15% TSP/PM10 ratio to the TSP data  from  the  five  large  dust  devils  sampled  in  1996  suggests  that  larger  examples  can  deliver  up  to  20  kg  of  fine  particulates  to  great  height.

References

Hall and Lemmon: Mass eject from Martian dust devils as functionof height and devil morphology