I have a block that I'd like monsters to break through, a little like doors. As a simpler alternative to the door implementation, I'm thinking that I'll make its collision box slightly smaller (like honey) and then slowly break the block whenever a monster is 'inside' it. However, I'm not sure how I should slowly break a block: I can destroy it or change the block at its position, but I don't know how to use the normal mining-progress system. All the methods I can find seem to be tailored specifically to a player intentionally mining the block, rather than being something I can just call whenever a condition is satisfied. What approaches should I look into?

I think a good starting point, as you already mentioned it, is to look at Zombie entity class and see what happens when the Zombie starts breaking a door. Specifically you can look at the BreakDoorGoal class that is used by the Zombie. Inside it, in the tick method, you will find this line

this.mob.level.destroyBlockProgress(this.mob.getId(), this.doorPos, i);

Essentially the function destroyBlockProgress is called by the zombie on its world (level) instance. I'm not sure if this is the actual method that shows the breaking overlay and also what values the last parameter (progress) should have, but by the name is definitively something I would try and see what it does

Here's my code. This works fairly well.

    protected int breakTime = 0;
    protected int lastBreakProgress = -1;
    protected int timeToBreak = 200; //10-second break time
    
    public void entityInside(BlockState state, Level level, BlockPos pos, Entity entity) {
        if (entity instanceof Monster) {

            ++this.breakTime;
            int i = (int)((float)this.breakTime / (float)this.timeToBreak * 10.0F);
            if (i != this.lastBreakProgress) {
                entity.level.destroyBlockProgress(entity.getId(), pos, i);
                this.lastBreakProgress = i;
            }

            if (breakTime == timeToBreak) {
                level.destroyBlock(pos, true);
                this.breakTime = 0;
            }

        }

        super.entityInside(state, level, pos, entity);
    }

 

...that would explain some lingering weirdness. Block entity it is, then.