ENH: Add core manipulation and coordinate methods to DataTree

[Shikhar-Kesharwani]

What does this PR do?

Resolves #10015 (DataTree: missing methods)
Resolves #9472 (DataTree.assign_coords and similar should only set node coords)
Resolves #9336 (DataTree.drop_vars)

This PR implements core data manipulation, missing value handling, array operations, coordinate assignment, and variable/dimension dropping methods on DataTree:

1. Dimension Manipulation & Reshaping

• DataTree.transpose(*dim, missing_dims="raise"): Transposes dimensions across all nodes in the tree. Supports custom dimension ordering, handles tree-wide dimension checks via _get_all_dims(), respects missing_dims ("raise", "warn", "ignore"), and supports trees with groups containing heterogeneous subsets of dimensions.
• DataTree.squeeze(dim=None, drop=False, axis=None): Squeezes length-1 dimensions across the tree using self.isel(drop=drop, missing_dims="ignore", **{d: 0}).
• DataTree.broadcast_like(other, exclude=None): Broadcasts the tree against another DataTree (by path matching) or Dataset/DataArray.

2. Missing Value Handling

• DataTree.dropna(dim, *, how="any", thresh=None, subset=None): Computes a tree-wide non-NA mask along dim across data variables in all nodes containing dim, then indexes via self.isel({dim: mask}). This guarantees parent and child nodes remain strictly aligned along shared and inherited coordinates without misalignment or duplicate coordinate errors.
• DataTree.fillna(value): Fills missing values with scalars, arrays, or variable-keyed dictionaries across all groups.

3. Array Operations & Filtering

• DataTree.clip(min=None, max=None, *, keep_attrs=None): Limits values in numeric variables across all groups to [min, max].
• DataTree.isin(test_elements): Tests element membership across the tree, returning a boolean DataTree.
• DataTree.where(cond, other=dtypes.NA, drop=False): Filters elements across the tree according to cond. Correctly resolves relative paths (including path == ".") when both caller and condition are DataTree objects.
• DataTree.pad(pad_width=None, mode="constant", ...): Pads arrays along specified dimensions across groups.
• DataTree.roll(shifts=None, roll_coords=None, **shifts_kwargs): Rolls arrays along dimensions across groups.
• DataTree.shift(shifts=None, fill_value=dtypes.NA, **shifts_kwargs): Shifts arrays along dimensions across groups.

4. Node Coordinates & Attributes (Addresses #9472, #9336)

• DataTree.assign_coords(coords=None, **coords_kwargs): Assigns coordinates to the specific target node. As discussed in DataTree.assign_coords and similar should only set node coords #9472, this avoids attempting to redundantly map over child nodes; instead, child nodes naturally inherit indexed coordinates.
• DataTree.assign_attrs(*args, **kwargs): Assigns attributes to the node, returning a new tree.
• DataTree.drop_attrs(): Clears attributes on the node.
• DataTree.drop_vars(names, *, errors="raise"): Drops variables across groups in the tree. Resolves datatree: drop_vars issue? #9336.
• DataTree.drop_dims(drop_dims, *, errors="raise"): Drops dimensions and their associated variables across groups.

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Tests

Added comprehensive test suite TestDataTreeManipulationMethods in xarray/tests/test_datatree.py covering all 16 methods, multi-node trees, varying node dimensions, error conditions, and coordinate inheritance verification (100% pass rate locally).