floor tile
甃 centers on a floor tile, specifically a flat piece of baked clay or stone used for paving or flooring.
甃 combines 秋 (autumn) and 瓦 (tile). The exact historical development is uncertain, but it likely relates to tiles used in construction, possibly with 秋 contributing a phonetic element.
Imagine autumn leaves falling onto a clay roof tile, but here the tile is on the floor: 秋 on top of 瓦 suggests a floor tile made of baked clay, like those used in traditional paving.
For シュウ, picture a shoe stepping onto a floor tile: shoe -> シュウ, and the tile is underfoot.