[BIP Proposal] Add sp() output descriptor format for BIP352

A significant focus has been placed on enhancing wallet interoperability and the efficiency of backup and recovery processes through a Bitcoin Improvement Proposal (BIP) which introduces a novel top-level script expression, sp(). This mechanism aims to facilitate silent payments by generating outputs through combinations of specified key material with sender input public keys. The proposal offers a foundational step toward improving the security and reliability of transactions within the Bitcoin network.

Further analysis delves into the practicality and implications of incorporating block height as a parameter in wallet descriptors to alleviate scanning burdens. While this idea offers a potential reduction in computational requirements, it also raises questions about its necessity given existing functionalities like "wallet birthday" and concerns regarding consistency across wallet features. Additionally, the management of BIP352 labels is scrutinized, with suggestions aimed at streamlining the recovery process by limiting the number of labels required for scanning, thus simplifying fund recovery strategies.

The dialogue extends to the challenges and opportunities presented by Taproot implementation and silent payment addresses. The computational demands associated with matching outputs for all eligible public keys as the blockchain grows are highlighted, alongside the limitations imposed by the maximum number of labels that can be scanned during the recovery process. Proposals for using specific key formats and expressions, such as "sp(scankey,spendkey)", for silent payments are discussed, emphasizing their benefits in terms of clarity, error detection, and user experience.

An intriguing approach to enhancing descriptor strings for third-party scanning servers involves incorporating the descriptor's birthday, aiming to provide essential information for determining the starting height for scanning. However, this proposal faces skepticism regarding the necessity and potential complications of introducing new key formats. Despite these reservations, there's an openness to maintaining simplicity and familiarity in the evolution of silent payment descriptors, with suggestions for encoding multiple labels within a single 64-bit number to streamline the process.

Lastly, an insightful message from Sebastian on the Bitcoin Development Mailing List challenges the notion that label scanning doesn't scale, proposing an alternative scanning method that leverages a label cache for efficient lookup. This method demonstrates scalability and efficiency, even with a large number of labels, suggesting that full-node wallets with specialized use cases could manage extensive label quantities without performance degradation. The ongoing debate reflects a collective effort to balance innovation with practicality and security in the development of Bitcoin's infrastructure.