Large account sync optimizations followups

Mirror of [2038](https://github.com/0xMiden/miden-client/issues/2038)

Refactor and improve documentation of idxdb .

- `apply_state_sync` function is too large and should be splitted into separate parts. https://github.com/0xMiden/miden-client/pull/1916#discussion_r3081567087
- Improve documentation. https://github.com/0xMiden/miden-client/pull/1916#discussion_r3081610509
- Make updates atomic (discovered here but present before). https://github.com/0xMiden/miden-client/pull/1916#discussion_r3060724369
- Transaction and sync updates share lot's of code. On `crates/idxdb-store/src/sync/mod.rs:217-289` & `crates/idxdb-store/src/transaction/mod.rs:119-201`.

The issue points to specific code sections in `crates/idxdb-store/src/sync/mod.rs` and `crates/idxdb-store/src/transaction/mod.rs`. Start by examining the `apply_state_sync` function and the overlapping code between transaction and sync updates. Review the linked PR discussions to understand the required refactoring and documentation improvements. The goal is to split the large function, improve documentation, and make updates atomic.

Vom Indexierungsmodell aus dem Issue-Text verfasst.