@<1722061389024989184:profile|ResponsiveKoala38> It fixed the issue!

curl -XPOST -H 'Content-Type: application/json' 'localhost:9200/events-training_debug_image-*/_update_by_query?conflicts=proceed' -d'{
    "script": {
        "source": "ctx._source.url = ctx._source.url.replace('http://<MY_OLD_ADDRESS>', '

.<NEW_ADDRESS>')",
        "lang": "painless"
    },
    "query": {"prefix": {"url": {"value": "http://<MY_OLD_ADDRESS>"}}}
}'

It's the same request you provided just without "case_sensitive" option and with my endpoints @<1722061389024989184:profile|ResponsiveKoala38>

About the prefix part I think it should not matter. Just put your prefix instead of ' None .<ADDRESS>'

I figured it was something with syntax but I thought single ticks inside double quotes should work without escaping 😀