Complete wordpress idiot here.
How do I change just the individual text of these headers? What is causing the text to leak to the other columns(?).
Video recording of what is happening
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Looks like you are changing the template, which works as intended by rendering all instances that use that template with the text you entered.
It would appear that this is a list of posts.
Would it not be possible to use the post titles for this? Or do you still wish to manually alter the titles for this display?
For the former you should be able to use the Title block, it will automatically insert the post title.
For the latter you would have to edit the titles on the page that actually uses this template. (I.e. what you get if you click Edit Page, not Edit Site.)
Assuming you thought you were editing a post or a page instead of a template, one way to avoid mix-ups like that is to only edit content with a second account that only has the editor role. You will not be able to accidentally change a template when you believe you were editing a post, simply because you will not have access to the former functionality.