You were right in differentiating between Feature Impact and Tree-based Variable Importance - Feature Impact is permutatation-based and Tree-based Variable Importance is node-impurity based. Since they are calculated using different means, it is not expected that these two methods always produce the same result. Feature impact (or permutation importance) is model-agnostic and is available for all the models on the leaderboard whereas Tree-based Variable importance is only available for tree-based models.
Regarding your second question on Feature Effects sorted by Impact, the order of features on the left side in Feature Effects is based on Feature Impact. However, some feature types like Text are not displayed within Feature Effects because it has high cardinality. Hence, you may find fewer features in Feature Effects as compared to Feature Impact in some projects.
Let me know if the explanations clarify your questions.