Amazon Web Services – How static / elastic IP addresses work, and more specifically why they need an address by "region"

I'm looking at Google Cloud and AWS and when you select "reserve static IP address", you need to specify a region like us-east-1, and so on. I understand that the regions are different data centers, but I am not. know what is the process for IP addresses used with regard to domain names ….

Specifically, let's say you have a website such as mywebsite.com. I wonder how this is mapped to a static IP address, or even if it must be static and can be dynamic.

What I imagine up to now, is that there is a 1-1 correspondence between the IP address and the domain name. So mywebsite.com can be mapped to the world's only public static IP 123.123.123.123then load balancing to distribute it to a group of servers.

But what's missing from this understanding is knowing where the regions come in. If I want to "take care of different regions", so that requests are processed more quickly, I would imagine that servers would work in a region specific. These servers are all processing the domain request mywebsite.com. But what I do not understand, if there are multiple IP addresses (static IP addresses I guess), any mapping to the same domain, how does the thing choose which IP address to use. You wonder if it is physically based on interconnected systems. So, my request on my laptop for mywebsite.com go on my side to the WAN in the nearest area, saying, "Oh, I have to go to 123.123.123.123 for the eastern region, not 123.123.123.124 for the western region." Then the request is handled by local and other servers. I receive this final part.

What I miss is how it selects the appropriate IP address if there are multiple IP addresses associated with a domain, for support of multi-region optimization.