When the hospital have decided he is 'medically fit for discharge' he will be referred to the hospital discharge team and he will be allocated a social worker.
Next of kin has no 'legal' standing in terms of decision making if someone is felt to have lost capacity. If you don't have power of attorney then the social worker will be the decision maker over what course of action is in his 'best interests' after discharge. Even if you apply for deputyship it is likely that it will only be awarded for financial decision making and not for decisions about his care.
The social worker will do an assessment to determine what his care needs are. Due to covid and also a policy trend that was happing pre covid this may not be completed in hospital, he may be discharged to a care home under 'discharge to assess' rules.
Wherever this assessment takes place his eligibility for fully funded continuing healthcare will be considered. If he isn't eligible and it remains the responsibility of social services to arrange his care they will look at a range of options and decide what will best meet his needs.
What happens next depends on if he is financially assessed as being able to afford to pay for his care in full himself or if he will be in receipt of funding from the local authority.
If the local authority are paying for it then they will not consider 24 hour live in care at home unless his needs cannot be met elsewhere. If he can afford to pay for it then he/you can do what you like but if he lacks capacity to agree to this and you don't have access to his finances it could be tricky.
If he doesn't need 24 hour care and can return home then social services will look at carers visiting him at home, usually around 4 times a day.
A lot can change in six weeks though, I wouldn't be setting your heart on any particular pathway until you know how well he is doing at the point of being medically fit for discharge.