generating random pair key has standard?
Developers of reputable wallets use a suitable source of randomness and will generate a key in the whole range available, not restricted to some arbitrary small range.
So far as I know there is no standard (e.g. BIP) that specifies this. It is assumed knowledge.
For example see https://www.freecodecamp.org/news/how-to-generate-your-very-own-bitcoin-private-key-7ad0f4936e6c/