I would strongly recommend volunteering with an avian rescue organisation well before deciding to go the 'spares sanctuary route'.
People often refresh their flocks because layers have become non-productive. Once they reach this life stage, there are a 'ton' of medical problems that come with it and even if you do catch them early, there is no guarantee the bird will survive and your intervention may end up prolonging their suffering and you'll be required to make a quality of life call.
If you don't handle death well, or would be unable to cull a suffering pet you can't save, a rescue organisation is not for you.
As mentioned, you will have biosecurity concerns unless you have hectares between flocks, integration issues - if you have never managed flock integration, this is a very complicated and time-consuming process to do properly without putting undue stress on your birds.
Also, as several have mentioned, why are you intending to rehome your own birds? Sorry, but it comes off as if you are bored with them and can't help but wonder what will happen when you get bored of your rescues.
Do you feel it would be okay to have 13+ hens and only get 2-3 eggs a day? (Bit of an exaggeration, but older hens 'slow down', which you mentioned as a reason to refresh your flock, but also with older birds).
Are you good at poultry first-aid? Do you have contact with or know an avian vet? Are you familiar with symptoms of a sick hen and how to manage them in a critical state?
These are necessary skills when handling an aging flock. Their needs can be very different than pullets and chicks and improper care can lead to months long suffering and a slow death if you're unfamiliar with indentifying an issue until it's too late.
Do volunteer work - get experience around diseases and injured birds (without bringing it home to your flock) - and see how you feel about it then when you have a better understanding of how to manage these stressors.
I've done a lot of volunteer time and have enough skills to feel confident 'I' could handle something like this, but I wouldn't. I'd recommend enjoying and caring for your existing flock into their golden years and focus on their quality of life instead of disrupting what they have.