Make FORM's write path thread-safe independent of Phlex

[coderabbitai]

Summary

FORM's write path currently has no internal locking. It relies on Phlex registering the output node with concurrency::serial to serialize writes.

FORM must be thread-safe independently of Phlex scheduling. The write path does not need to be concurrent by default.

Required work

Add FORM-owned synchronization for the write path.

Possible solutions include write-path mutexes that follow the existing read-side mutex pattern:

• root_tbranch_read_mutex
• root_rfield_read_mutex

Audit other write-path call sites that require synchronization.

Scope

This issue is independent of #834, which tracks row-index handling for a future ROOT::RNTupleParallelWriter implementation.

Affected areas

• form/root_storage/
• ROOT write containers
• Storage and persistence writer call paths
• Write lifecycle operations such as setup, fill, and commit

Acceptance criteria

• FORM write operations are safe when callers invoke them from multiple threads.
• The implementation does not depend on Phlex concurrency::serial for correctness.
• The default implementation does not introduce concurrent writes unless explicitly designed to do so.
• The audit identifies and protects relevant write-path shared state.
• Tests cover the selected synchronization behavior.

References

• Pull request: Form: Return a Token from registerWrite #830
• Review thread: Form: Return a Token from registerWrite #830 (comment)

Requested by: @wwuoneway