[libc][tsearch] add weak AVL tree for tsearch implementation (#172411)

Related to #114695.

This PR adds a Weak AVL Tree for tsearch APIs. The symbol
implementations are coming in a
following up PR to avoid creating a huge patch. The work is based on
@MaskRay's recent post (see below).

A general self-balancing binary search tree where the node pointer can
be used as stable handles to the stored values.

The self-balancing strategy is the Weak AVL (WAVL) tree, based on the
following foundational references:
1. https://maskray.me/blog/2025-12-14-weak-avl-tree
2. https://reviews.freebsd.org/D25480
3. https://ics.uci.edu/~goodrich/teach/cs165/notes/WeakAVLTrees.pdf
4. https://dl.acm.org/doi/10.1145/2689412 (Rank-Balanced Trees)

WAVL trees belong to the rank-balanced binary search tree framework
(reference 4), alongside AVL and Red-Black trees.

Key Properties of WAVL Trees:
1. Relationship to Red-Black Trees: A WAVL tree can always be colored as
a
   Red-Black tree.
2. Relationship to AVL Trees: An AVL tree meets all the requirements of
a
WAVL tree. Insertion-only WAVL trees maintain the same structure as AVL
   trees.

Rank-Based Balancing:
In rank-balanced trees, each node is assigned a rank (conceptually
similar
to height). In AVL/WAVL, the rank difference between a parent and its
child is
strictly enforced to be either **1** or **2**.

- **AVL Trees:** Rank is equivalent to height. The strict condition is
that
there are no 2-2 nodes (a parent with rank difference 2 to both
children).
- **WAVL Trees:** The no 2-2 node rule is relaxed for internal nodes
during
the deletion fixup process, making WAVL trees less strictly balanced
than
  AVL trees but easier to maintain than Red-Black trees.

Balancing Mechanics (Promotion/Demotion):
- **Null nodes** are considered to have rank -1.
- **External/leaf nodes** have rank 0.
- **Insertion:** Inserting a node may create a situation where a parent
and
child
have the same rank (difference 0). This is fixed by **promoting** the
rank
of the parent and propagating the fix upwards using at most two
rotations
  (trinode fixup).
- **Deletion:** Deleting a node may result in a parent being 3 ranks
higher
than a child (difference 3). This is fixed by **demoting** the parent's
  rank and propagating the fix upwards.

Implementation Detail:
The rank is **implicitly** maintained. We never store the full rank.
Instead,
a 2-bit tag is used on each node to record the rank difference to each
child:
- Bit cleared (0) -> Rank difference is **1**.
- Bit set (1)     -> Rank difference is **2**.

---------

Co-authored-by: Michael Jones <michaelrj@google.com>
GitOrigin-RevId: db713325d530e88d0229643c6002950ddfc16d6e