Chemicals can leech out of landfills into water tables and waterways. Landfills can also emit greenhouse gasses. None of these happen as a result of burying shaving cartridges.

It's no different than the sand that's already below ground. It essentially just sits there.

The production and transportation of the cartridge could harm the environment though, but that's a more complicated story.

Shaving cartridges are mostly plastic, which does leech chemicals, including hormone mimics, into groundwater.

Any landfill made in the last 50yr has a sump and the liquid nastiness gets its own direct line to the local water treatment plant.

Likewise they capture or flare the methane.

Their production causes environmental harm. A small amount compared to other thing to be sure, but not "none".