When the worldborder expands slowly, it is possible to walk onto a block as soon as the border starts expanding into it. However, until the border catches up to your exact position within that block, you will take suffocation damage. This also applies to mobs, like bats flying into the border.

Expected behavior:

1. The area that players and mobs can move into is not rounded up to the nearest block.
2. Alternatively, the area in which players and mobs do not take suffocation damage is also rounded up to the nearest block.