Can the word "footing" be used in regards to an inanimate object?

As noted footing can be used idiomatically with objects or with collective nouns to refer to a stable posture or established placement. One could say "They moved the table where it would have sounder footing" or "The ambassador left trade negotiations on a sure footing."

In this case, however, I might suggest phrasing differently, as I think of a "toolbox" as a small, hand-carried box with a flat bottom— not something I would expect would need adjustment for stability, and for that matter not something I think of as "falling over" either as opposed to "falling off." Perhaps

The toolbox fell off the bench because it wasn't placed squarely.

The toolbox fell over the ledge because it was left dangling over it.

Firm footing as an idiom is used frequently, with reference to inanimate objects as well. Footing itself is an (inanimate) structural member in general engineering use.

The example sentence in the OP makes correct usage of solid footing.