When a server uses Havoc verification, you are asked to log in with Discord on this site once. Havoc asks for one permission: identify (who you are). Your login token is used once and then revoked.
Havoc does not save your IP address, browser or device information, linked accounts or server list. Nothing from this page is written to disk. The only thing remembered is that you linked, held in the bot's memory for 30 minutes so you can press verify, and it disappears after that or when the bot restarts.
Havoc is a moderation bot, so servers that use it keep their own moderation records (warnings, bans and similar cases) in Havoc's database. To spot alts it also compares public profile details of server members (username, avatar, banner, join time and invite). That is separate from this page.