[Bug] VAnchor proof fails with non-input leaves

[AhmedKorim]

Describe the bug

VAnchor proof is invalid while prooving against non-input leaves

• When the proof is valid?

  • With default input utxos
    Given the input Utxos, all are default, the root setup is [ActiveChain TreeRoot, Neighboring Tree Root], and the
    amounts match the role Sum(I) + Public amount = Sum(O).

  • All input commitments are on the leaves

To Reproduce
Steps to reproduce the behavior:
1- Construct a Merkle tree with already existing commitments.
2- Generate a valid VAnchor setup
- Sum of Input amount + public amount =Sum of output amount
- While the input has a non-default UTXO the commitment of that output should be in the MerkleTree

Expected behavior

• The proof should pass given a valid proof setup
• Valid roots, The root sets' first element matches the root of the supplied leaves, And the second element is the neighbor MT root
• Input Utxos commitments are in the tree with the right indices specified
• Sum(input Utxos) + public amount = Sum(output Utxos)
• the proof shouldn't just be valid if the input commitment (input Utxos) is the only leaves existing on the tree

Additional context
Tests
Check the branch ahmed/fix-vanchor-n-plus-withdraw

DApp flow
Deposit flow (2-2-2 fixtures)

• Crate a two empty Utxo for input amont =0 index =0
• Create the output Utxos [Utxo with full amount , Default Utxo]
• Fetch the tree root, the neighbour root and construct the root setup
• Use empty leaves map to generate the proof - After insertion Mutate the Non-default utxo index
  This is always passing

Withdraw flow (2-2-2 fixtures)

• For a given note - Fetch the leaves up to the leave
• Construct a Merkle tree and inset the leaves to get the Merkle root
• Fetch the neighbor root from the chain
• The output is calculated based on the amount to withdraw Input + (-amount) = Output
  This is passing for the first time only