How avoid jump line disappear when concat string [BASH]

I want to list all urls contain in all file of my project.

First function find_url_in_file, work well –> I have this list

https://www.example.com/en/docs/console/my-project/how-to/add-resources-project
https://www.example.com/en/docs/console/my-project/how-to/generate-api-key
https://www.example.com/en/docs/console/my-project/how-to/delete-a-project
https://www.example.com/en/docs/console/my-project/how-to/join-an-organization

Then with second function find_all_url_in_file, when it concat it remove all line jump :

https://www.example.com/en/docs/console/my-project/how-to/add-resources-projecthttps://www.example.com/en/docs/console/my-project/how-to/generate-api-keyhttps://www.example.com/en/docs/console/my-project/how-to/delete-a-projecthttps://www.example.com/en/docs/console/my-project/how-to/join-an-organization

I want to keep this line break to have a simple clean nice list. How could I do?
(maybe it’s a better idea to use a temp file ?)

all_mdx_file=$(find_all_mdx)

find_url_in_file(){
    local file=""
    local url_list=""
    grep -Eo '(http|https)://www.xxxxxx.com[^ )>"]+' $file || : | 
    while IFS= read -r url; do 
        url_list+="$url"
    done
    echo "$url_list"
}

find_all_url_in_file(){
    local file=""
    local list_url=""
    while IFS= read -r mdx; do 
        # echo "mdx read : $mdx"
        url_in_this_file=$(find_url_in_file $mdx )
        list_url+="$url_in_this_file "
    done <<< "$file"
}

find_all_url_in_file "$all_mdx_file"