Bug: MarkdownHeaderSplitter shares parent_headers list across secondary chunks when keep_headers=False

Describe the bug
When MarkdownHeaderSplitter runs with keep_headers=False and a secondary_split (e.g. "word"), every secondary chunk produced from the same header section shares the same parent_headers list object. Mutating one chunk's parent_headers leaks into its siblings (same shape as #12248 / #12424, but on a conditional path those PRs did not cover).

Error message
No error; the metadata is silently aliased.

Expected behavior
Each chunk gets its own copy of parent_headers (as already happens with keep_headers=True + secondary split, and as #12424 did for PythonCodeSplitter). Editing one chunk must not affect its siblings.

To Reproduce

from haystack import Document
from haystack.components.preprocessors.markdown_header_splitter import MarkdownHeaderSplitter

text = "# Top\n\n## Section A\n\n" + "word " * 100
sp = MarkdownHeaderSplitter(keep_headers=False, secondary_split="word", split_length=10, split_overlap=0)
sp.warm_up()
out = sp.run(documents=[Document(content=text, meta={"tags": ["orig"]} )])["documents"]
print(len(out))  # >1 from the same Section A parent
print(out[0].meta["parent_headers"] is out[1].meta["parent_headers"])  # True (bug; expect False)
out[0].meta["parent_headers"].append("MUT")
print(out[1].meta["parent_headers"])  # ['Top', 'MUT'] (bug; expect ['Top'])

Verified on main @ 5bf0ffc (v3.2.0-rc0): with keep_headers=True the identity check is False and the mutation does not leak; with keep_headers=False it is True and leaks. tags (deep-copied by the secondary DocumentSplitter) is safe in both modes, so only the header-preservation overwrite leaks.

Additional context
Root cause in haystack/components/preprocessors/markdown_header_splitter.py _apply_secondary_splitting (~L277-279 on origin/main):

if not self.keep_headers:
    for key in ["header", "parent_headers"]:
        if key in doc.meta:
            split.meta[key] = doc.meta[key]  # shares the list object across all secondary siblings

The secondary DocumentSplitter already deep-copies each chunk's meta, but this loop then overwrites parent_headers with the parent doc's list reference, discarding the distinct copies. header is a str (safe); parent_headers is a list (unsafe).

Sibling history (not duplicates): #12248 (family issue) -> #12249 fixed Markdown/CSV/hierarchical; #12424 fixed PythonCodeSplitter and stated the family was closed after checking the remaining splitters. This site was missed because it only triggers when both keep_headers=False and secondary_split are set. Distinct from #12618/#12619 (page_number drift with overlap) and #12477 (leading-header loss).

Possible fixes:
a) (Recommended, minimal, matches #12424 pattern) split.meta[key] = deepcopy(doc.meta[key]) at the overwrite site -- deepcopy is already imported in this file.
b) Copy just the list (list(...)) for parent_headers -- narrower but leaves any deeper nesting shared.
c) Deep-copy clean_meta upfront and keep the overwrite deep-copied -- redundant; (a) alone suffices since the secondary outputs are otherwise already distinct.

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System:

• OS: macOS
• Haystack version: main @ 5bf0ffc (VERSION.txt 3.2.0-rc0), Python 3.11