why does my url not update after migration?

When editing content in the content editor WordPress hardcodes the current URL that is being used to access the WordPress admin. This is usually found in link href and image src. There are several plugins or tools (like wp-cli) that can assist you in finding and replacing the url between environments.

You will likely want to your search to look something like:

Old
//site1.com

New
//site2.com

NO TRAILING SLASH in the search! Don’t use the protocol if you are not trying to switch/normalize urls from http to https, same goes for www domain variants.

If you access the site at several different domains during the development cycle you may want to look into tools like the WordPress plugin WP Migrate DB Pro that find and replace while migrating between environments or manually on the current environment.