assemble
聚 centers on bringing separate things together into one group: assembling, gathering, or collecting.
聚 combines 取 (take) and 乑 (a variant of 众, meaning many people), suggesting taking many people together into one place. The exact historical development is uncertain, but the component combination fits the meaning of assembling.
The top 取 means 'take', and the bottom 乑 looks like a crowd of people. Imagine taking a crowd and assembling them in one spot.
For シュウ, picture a shoe factory where workers assemble shoes: shoe -> シュウ, and the workers gather together to build them.
Wamyōruijushō (famous Heian-period Japanese dictionary)
collection and distribution
(levying of a) heavy taxation
grey wall covering material (gray)
collection of similar objects; classification by similarity
Ruijū Myōgishō (Japanese-Chinese character dictionary from the late Heian Period)