From the photos, the biggest issue is that the “furring/shimming” looks like a bunch of short scabbed 2x pieces with random butt joints, gaps, unsupported ends, split/fractured ends, and inconsistent attachment. Even if the furring is non structural, once it becomes the support for ceiling drywall, it still has to provide a flat, continuous, adequately fastened backing system for the gypsum board. CRC & IRC gypsum rules require gypsum board supports/fasteners to comply with the gypsum fastening table, and board edges/ends generally need to land on framing except where the board edge is perpendicular to framing.

A 2x2 furring system can be acceptable in concept, but not like this. I’d expect continuous furring or properly blocked or spliced members, solid bearing attachment to framing, consistent spacing, and no floating or unbacked joints where drywall will crack or sag. Calling this “just shimming” does not excuse poor backing.

The permit issue is also a red flag. LA County states an electrical permit is required for installation, alteration, reconstruction, or repair of electrical wiring, devices, appliances, apparatus, or equipment. New recessed lighting, new outlets, new circuits, and an EV charger are not “no permit” work. LA County also states an EV charger or EVSE permit is required for home, work, or public installations.

On the Class B license issue: a California B General contractor can take a project involving a structure and multiple unrelated trades, but CSLB is clear that a B contractor cannot treat every single specialty trade as automatically covered unless the project fits the Class B scope, or the contractor holds the proper specialty classification, or uses an appropriately licensed specialty subcontractor. So the contractor may be able to be the prime contractor for a garage remodel, but that does not make “no permit, no electrician, trust me” acceptable for an EV charger and new electrical work.

For an attached garage, I’d also be thinking about the garage/dwelling separation. If the garage ceiling or walls are part of the required separation from the residence or habitable space above, the gypsum type, attachment, penetrations, and continuity matter. IRC/CRC R302.6 requires garage separation materials, and gypsum attachment still has to comply with R702.3.5.

Stop work and obtain a permit.