Is domain renewal cost included in iCloud+ subscription?

I think I may have been confused about this, but maybe not...

When I started my paid for iCloud+ subscription, I 'imported' my own domain to use it within iCloud, rather than paying someone else to host it, essentially to save a bit of money.

I thought the monthly subscription included the cost of the domain, but 123.reg have just advised me I need to update my payment card to pay for the renewal. It's not a spam email massage, as far as I can tell.

Simply put, should I be paying 123.reg for the renewal cost of the domain, or is this cost 'covered' by my iCloud subscription?

Thanks.

[Re-Titled by Moderator]

Original Title: iCloud+ own domain