I have been reading the new SEP and seeing error code getting chosen out of nowhere, but shouldn't a protocol formalise this, even projects like postgres do this.

A workable formal classing scheme (within -32000..-32099)
Because we only have 100 slots, the most practical structure is two digits:

• -32 C R → C = class (0–9), R = reason (0–9)
• Example: -32042 → class 4, reason 2

Suggested class map (example):

• 0x: General / common
• 1x: Auth / access
• 2x: Not found / missing
• 3x: Validation / state
• 4x: Interaction / elicitation
• 5x: Rate limit / quota
• 6x: Transport / upstream
• 7x: Capability / negotiation
• 8x: Data integrity / tamper
• 9x: Reserved / experimental

it will also help people reason about the error and it's impact , although all error code has same client impact.