The 'management' address won't be used as the source addrrss packets originating _from_ the host unless the use of temporary/privacy addresses is disabled.
A friend assigned ::25 for the service vIP of his SMTP server/process, and ::143 for IMAP. Your web(mail) host could be ::80 and/or ::443. All on the same host (if you wish). If you have an HA setup you can have the vIP failover by using (e.g.) keepalived.
Using tokens may be of some interest as well:
* https://man7.org/linux/man-pages/man8/ip-token.8.html
You can have a public prefix address, as well as a local 'private' ULA address at the same time. In some ways I wish the best practice would be for IoT devices and appliances (like printers) only have link-local addresses, and perhaps ULA if advertised, with global addresses only configured via config switch. It would perhaps allay some the concerns that people have (like you do).
I think most OSes do that privacy thing where they periodically randomize the suffix of their v6 address.