From a copyright perspective, the content and the design of a website are two different, independent things. It is certainly possible to have the content under a different license than the design. You just have to look at the Stack Exchange site, where the content is under the CC BY-SA 3.0 license, but the design is under a closed source license.
The MIT license on your theme is a very permissive license. The only real requirement is has is that you don't delete the license text and accompanying copyright information. If all of that is just in comment blocks or a separate license file, you don't even have to mention the license and copyright visibly on your site (although it can be a sign of goodwill to do it anyway).
You could put something like this on your site:
Content: Copyright 2023 John Karkas. All rights reserved.
Design: Copyright 2023 John Karkas. All rights reserved; Based on MIT-licensed theme <link>.