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The tags , H1, H2 and so on are not visible while writing the post which makes it difficult to write the post.Its visible in preview,but not while editing it.
In the below image, I have made the headlines BOLD for easier understanding.
I have tried:
1. Checking the visual editor is on/off: It's ON
2. Disabling plugin.
3. Theme switch to check if the problem is with the theme: Negative.
Help is much appreciated.

There can be many issues. Maybe the issue is with the theme or maybe its the caching plugin. You need to disable plugins one by one and check which one is the issue. Another reason can be that your hosting provider has limited some features like limited ram or using old versions of php etc which can cause such issues.
If it’s visible in preview but not the editor, the styles for headings are most likely only being called on the front end, not the admin area. It might be an issue with the theme you’re using and how it renders the markup.
Did you add custom CSS to the headings outside of the “theme settings” controls? Possible that’s what it isn’t picking up. Anything set in the “style settings” should be picked up fine in the editor.