Compromised password message on my iPhone

Yes, it is real. Note that there is no scam link in it. Go to Settings/Passwords/Security Recommendations to see this and other potentially compromised passwords.

Apple and other tech companies monitor the “dark web” for compromised personal data from hacked businesses, and create lists of compromised IDs, passwords, and other data, then match it against user-saved credentials. Here is a public site that lets you search for your own IDs and passwords→https://haveibeenpwned.com