I'm surprised that we don't seem to already have a Meta question about this specifically.
You claim your posts by linking your Codidact account with your Stack Exchange account. To do that, click on your avatar in the top bar to go to your profile, then the "Edit" tab, and then look under the "Link with Stack Exchange" heading. You will need to do this from a site that has a corresponding Stack Exchange site, such as Writing or Scientific Speculation, but the link is actually made between your Codidact network account and your Stack Exchange network account, so you only need to link once and it will apply to all sites where content is imported from Stack Exchange, historically or in the future.
You will need to grant permission over on Stack Exchange for Codidact to access your account data (I don't recall the exact phrasing, but they'll ask you for confirmation that you want to do it). However, that's only needed for the linking process itself, so if you want, you can go into your Stack Exchange profile immediately afterward and revoke that permission; it's not needed for future use of Codidact.
Once you have linked your accounts, your posts will be claimed by the Codidact account that you link to your Stack Exchange account, the "holder" account will be removed as it no longer serves any purpose, the import notice will be removed from your posts, and you will be able to interact normally with those posts on Codidact.