Realtime Database 250KB write limit: does it apply per path in a multi-path update or to the whole payload

Goal

I am designing a data layer on Firebase Realtime Database that fans out one logical change across several locations using a single multi-path update (an atomic update() call with multiple paths). I need to understand exactly how the documented 256MB database / per-write size constraints apply so I can decide whether to split large updates into multiple calls.

Constraints and uncertainty

The documentation describes a maximum size for an individual write operation (commonly cited around 256MB total stored data and a per-write payload ceiling in the hundreds of KB range). What is unclear to me is how that ceiling is evaluated for a multi-path update: is the limit checked against the serialized size of the entire update map, or per individual path value? I also want to know how this interacts with the documented per-connection write rate, since splitting one atomic update into several writes would sacrifice atomicity.

Questions

1. For a multi-path update(), is the write size limit enforced on the combined payload or on each path's value separately?
2. If the combined payload exceeds the limit, does the entire update fail atomically, and with what client-observable behavior?
3. Does the limit differ between the client SDKs and the Admin SDK, and between Spark and Blaze plans?