NGINX reverse proxy relative links, issue with routed location - nginx

Question

So I have 2 docker containers running different Flask apps, port forwarded to the host. The host has a NGINX server redirecting requests to the server to the respective containers. The "sites available" file for the NGINX server is as shown:
server {
root /var/www/myserver/html;
index index.html index.htm index.nginx-debian.html;
# Don't forget to include .com below!
server_name myserver.com www.myserver.com;
location / {
proxy_pass http://127.0.0.1:6789/;
} # Here, we reverse proxy the port 80 to port 6789, where the website is served by Docker
location /smallblog/ {
rewrite ^/smallblog/(.*) /$1 break;
proxy_set_header Host $host;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header X-Forwarded-Proto $scheme;
proxy_set_header X-Forwarded-Host $host;
proxy_set_header X-Forwarded-Port $server_port;
proxy_pass http://127.0.0.1:8000/;
proxy_pass_request_headers on;
} # Here, we reverse proxy the port 80 with /smallblog route to port 8000, where the smallblog is also served by another Docker container
listen [::]:443 ssl ipv6only=on; # managed by Certbot
listen 443 ssl; # managed by Certbot
ssl_certificate /etc/letsencrypt/live/myserver.com/fullchain.pem; # managed by Certbot
ssl_certificate_key /etc/letsencrypt/live/myserver.com/privkey.pem; # managed by Certbot
include /etc/letsencrypt/options-ssl-nginx.conf; # managed by Certbot
ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; # managed by Certbot
}
server {
if ($host = www.myserver.com) {
return 301 https://$host$request_uri;
} # managed by Certbot
if ($host = myserver.com) {
return 301 https://$host$request_uri;
} # managed by Certbot
listen 80;
listen [::]:80;
server_name myserver.com www.myserver.com;
return 404; # managed by Certbot
}
With this configuration, accessing www.myserver.com/smallblog indeed gives the right page. But, all links inside that page point to the myserver.com, for example a link to login page is www.myserver.com/login instead of www.myserver.com/smallblog/login. And all internal relative links (e.g. javascript links) don't work. Is there a way to solve this?
Buit if I use the / location in the script above to serve smallblog instead, this issue doesn't exist. So I figure there must be a way I don't see.