How to prove there is no direct effect in a mediation model? This answer states that the analysis done through the R mediation package:

isn't designed to prove that there is no direct effect, but rather show that there is one. Your insignificant estimate for the ADE reflects a lack of evidence, not contrary evidence per se.

So how can I prove that there is no direct effect in a model?

You are looking for a test for equivalence (general to statistical inference, and not restricted to mediation analysis). A simple approach is to use two one-sided tests for equivalence. Uniformly most powerful tests for equivalence are a more sophisticated approach.
Generally, one chooses a minimum magnitude of difference $\delta$ that you care about (i.e. a minimum effect size): any difference $\delta$ or smaller indicates quantities which are equivalent for your purposes. The null hypothesis for a test for equivalence is $\text{H}_{0}\text{: } |\theta| \ge \delta$. (In plain language "the magnitude of the difference between quantities is at least as big as $\delta$.") And the alternative hypothesis for a test for equivalence test $\text{H}_{\text{A}}\text{: } |\theta| < \delta$. (In plain language "the magnitude of the difference between quantities is smaller than $\delta$.") If one rejects $\text{H}_0$, then you have found evidence that $\theta < \delta$ and $\theta > -\delta$. I.e. you have found evidence that $-\delta < \theta < \delta$.
One can express this equivalence interval asymmetrically (often used for asymmetrically-scaled measures, such as odds ratios, etc.).
Finally, you can also combine inference from a test for difference with a test for equivalence (and thereby guard against confirmation bias). See the 2×2 table in my answer for the logic of combined inference in so-called relevance tests.
Some useful references
Hauck, W. W., & Anderson, S. (1984). A new statistical procedure for testing equivalence in two-group comparative bioavailability trials. Journal of Pharmacokinetics and Pharmacodynamics, 12(1), 83–91.
Schuirmann, D. A. (1987). A Comparison of the Two One-Sided Tests Procedure and the Power Approach for Assessing the Equivalence of Average Bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680.
Wellek, S. (2010). Testing Statistical Hypotheses of Equivalence and Noninferiority (Second Edition). Chapman and Hall/CRC Press.
