Turbo morphing will allow to do exactly that, exclude a section from morphing, by wrapping it in:

<div data-turbo-permanent>...</div>

I think it's not yet documented since turbo has not yet landed in a production release of Turbo but it's been merged into main, you can see it mentioned on the PR: https://github.com/hotwired/turbo/pull/1019 (Look for "Exclude sections from morphing" title in the PR description).