Sorry, NotJustKangaskhan, I don't want to be argumentative but ...
I thought it best to specify who is requiring it and what they typically think. It will be the Elective Home [Education Officer] who assesses
The thing is that no-one is charged with carrying out such an assessment. It is always the parent's duty to ensure a child receives an education (Education Act 1996, s7). Unless there is reason to think that the parent is failing in that duty (Education Act 1996, s437), the LA need do nothing.
they thankfully have to keep biases to themselves and be happy as long as there is evidence of any type of education
They also need no evidence - s437 is worded negatively (if it appears that no education is being provided).
You also don't have to join any home education organization or groups
I agree. Most local groups do not require you to be in an organization in order to go along and chat to other EHE parents,
If you feel he is already at that level, then look into ways to maintain his current level
I'd be very worried if a 7yo had merely "maintained the level" (whatever that means) that he was at at 5yo. In EHE, those terms are rather meaningless as there is no agreed level or set of knowledge that a 7yo should have. I agree, however, that someone intending putting a child into school at 7 should probably find out what the school will expect and try to tick off those expectations in the six months or so before starting at the school.
non-academic areas he may need to work on or he feels he wants to improve (such as emotional skills, social skills, mental skills like memory and focus).
I'm boggling somewhat at the idea of a 5yo who specifically wants to improve those things. I also think it would be very difficult for a 5-7yo not to improve in those areas. If I were the OP, I'd want to spend the next 18 months educating my child to his ability and aptitude rather than thinking about what a school would want. Given what the OP says, I'd be quite surprised if school would be a much better fit in two years - they may well decide to continue in EHE.