Given all preparatory work described in T151307, and in particular introducing the DispatchingPropertyInfoLookup class in T152103 we could now make property info related code in ClientStore/WikibaseStore work with foreign properties too.
I believe there would be one extra step needed: ClientStore interface provides PropertyInfoStore (more specific interface extending PropertyIInfoLookup) instance to the WikibaseClient. We could introduce DispatchingPropertyInfoStore that would use DispatchingPropertyInfoLookup instance for read operations, and a "usual" PropertyInfoStore implementation (PropertyInfoTable/CachingPropertyInfoStore) for write operation on local repo. It should deny doing any write operations on properties from foreign repositories.
Implementation note: it probably makes sense that single instance is used for read and write operations on local repo, and there is no separate write and read service for this repo.