Trash bin in the countertop

A countertop is usually sealed with silicone, which is applied thinly to the open areas

Not quite right, because the silicone should be massaged in to seal the pores of the chipboard. Just as well, waterproof glue can also be used, for example.
In the case of the OP, not applicable because the surfaces will probably stick together over time due to the conical cutout.
The real danger does not come from the board itself, because it is already waterproofly laminated if it is high-quality. The problem lies between the board and its coating, which must be sealed, and this is best achieved when the cutout is virtually wrapped. This works quite well with power tape and a silicone seam that is then made around a sink. I would consider this almost 100% sustainable. Here is an example of how it can look then: