How can I put a contact form in my post content?

The simplest and recommended way is to use the contact form selector block. In the WordPress block editor screen, select the Contact Form 7 block with the familiar mountain icon, then choose the contact form to put in.

Screenshot of the block selector modal.
Screenshot of the block selector modal.

Also, the traditional way using the WordPress shortcode is still available. In this case, you need to manually copy the shortcode of the contact form and paste it into the post content. Use the Shortcode block if you use the block editor.

Just another contact form plugin for WordPress. Simple but flexible.