How does proxy_redirect correctly replace the Location URL?

Question

I am using the following Nginx reverse proxy configuration.

server {
    listen      80;
    listen      [::]:80;
    server_name www.example.com;
    location / {
        proxy_pass http://127.0.0.1:3000;
        proxy_set_header Host $Host;
        proxy_set_header x-forwarded-for $remote_addr;
        proxy_set_header X-Real-IP $remote_addr;
        add_header Cache-Control no-store;
        add_header Pragma no-cache;
        proxy_http_version 1.1;
        proxy_set_header Connection "";
    }
}

The vast majority of the time, it works well. However, problems occur when visiting URLs that have 301 redirects set.

For example, when visiting http://www.example.com/aaa/, it should redirect to http://www.example.com/bbb/

but it redirects incorrectly to http://127.0.0.1:3000/bbb/

After investigating this issue, I found that I should use the proxy_redirect parameter instead.

I found a description of proxy_redirect on the Nginx website, but I'm sorry that I didn't fully understand it.

As I understand it, the following usage can be used to solve my problem. The reason for not using a regular expression to get the rest of the URL is that it is automatically appended to the replacement string (am I right?) .

proxy_redirect http://$proxy_host/ /;

I also have two questions.

1、For non-80 ports, the $proxy_host variable should also output the port, something like 127.0.0.1:3000. But why does the official Nginx example use http://$proxy_host:8000/, is this a bug? Or is there something I'm not understanding?

2、Suppose that accessing http://www.example.com is incorrectly redirected to http://127.0.0.1:3000. In this case, does the above substitution syntax not work, because its substitution condition is at least http://127.0.0.1:3000/ (the / character is missing). How should I solve this problem? Should I use a regular expression to get the full URL for replacement? If so, is the following syntax correct?

proxy_redirect ~*http://127.0.0.1:3000(.*)$ http://www.example.com$1;

Thank you for your patience in reading, and thanks in advance!