Various products are available specifically for leveling a device in an oversized opening, such as this bracket.
Selection at big box stores may be limited, go to an electrical supply house if you can't find similar.
You can use spacer shims, they're available at most electrical supply, hardware, and big box stores. They're also available from various manufacturers.
Your excellent picture shows the three score marks on each end of the receptacle. These are there for the expressed purpose of breaking off the ends by bending back and forth with pliers.
The pieces with the holes are to be used as shims to space out the receptacle if the box is too far in. The center piece (no hole) is to be removed so the end does not rest on the wall surface but only on the box. Use one or both shims on each end as necessary to allow spacing out the receptacle up to 1/8". This gives a securely held receptacle spaced at the right distance relative to the wall surface.
If the wiring is in metal conduit and metal boxes are used, then the grounding of the receptacles may be accomplished by secure contact of the ends of the receptacles with the box. The metal shims make a conducting connection whereas plastic ones do not. There would be a conduction path through the threads of the screws, but according to code this is not acceptable by itself as a grounding connection.
In the case here the boxes are plastic and grounding is by a wire to the grounding screw. Hence there is no point to having high conductance of the shims. The plastic shims are more convenient to use because the plastic shims are designed so that the screws don't have to be fully backed out to insert the shims. The metal shims are however stronger and might outlast the plastic ones.