This thread is resolved. Here is a description of the problem and solution.
Problem: I can't see my Contact Forms 7 in the backend list.
Solution: Go to WPML > Translation management > Multilingual content setup and scroll down to "Custom post types" section. Check if "Forms" is set to "Do nothing" (because Contact forms should not be translatable).
More details about using Contact Form 7 with WPML: https://wpml.org/documentation/plugins-compatibility/using-contact-form-7-with-wpml/
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