Marriage proposal

I don't understand how you can allow it with difficulty? Isn't there a "don't come near" here?

Because it is not clear that this is included in the prohibition. The question is whether this leads to incest or at least provokes forbidden thoughts. Thus, the Rambam in the Rish Pacha of the Prohibitions of Intimacy:

Anyone who comes to a nakedness from incest through the limbs or who embraces and kisses through lust and enjoys close flesh is in violation of the Torah, as it is said not to do the imitations of abominations, etc., and it is said that you shall not come near to expose nakedness, meaning that you shall not come near to things that lead to incest.

And, indeed, we are talking about closeness “through lust.” This is indeed the definition of the Torah, and in the rabbis there may be a place for prohibition even without this. But we are still talking about closeness that leads to incest (even if there is currently no lust in it). And thus the words of Rav Pedat are explained in Gemara 7:17:1 and Shabbat 13:1 and see the appendix there and there.

And the words of Ritva at the end of Kiddushin are also known:
Everything is according to the will of God. And so the way of life is according to what a person knows for himself, if it is appropriate for him to distance himself from his desire, he does it, and even looking at a woman's colorful clothes is forbidden, as is stated in Tractate Avoda Zara (22:2), and if he knows for himself that his desire has surrendered and is subject to it and does not harbor any grudge, he is permitted to look at and speak with the nakedness and ask about the peace of a man's wife, and that is what Rabbi Yochanan (22:44) said of Ash'ari, who bathed and did not hesitate to think about the evil desire, and Rabbi Ami Denfaki said of her, "Amma'ta Debi Caesar" (Ketubot 17:1), and several of the rabbis of the Demishta tribe, who are also Matronyta (above 4:1), and Rav Ada bar Ahavah, who said in Ketubot (ibid.), "He covered her shoulders and danced in her and did not hesitate to contemplate her." From what they said, but it is only appropriate to be lenient in this for a great Hasid who recognizes his inclination, and not all scholars of Torah trust in their inclinations as much as they do in listening to all that they worship in their imaginations, and blessed is he who overcomes his inclinations and his labor and training in the Torah, for the words of the Torah stand for a person in his childhood and give him a future and hope in his old age, as it is said, "They will again be fruitful and will be fresh."

And all this is just a woman. And here it is about the person who will be his wife, there is room for more leniency (especially if this is perceived as part of the ceremony/status). But as I wrote, all of this is an excessive allowance and in my opinion it is not appropriate to act in this way in practice.

Towards Leah? On the contrary, in the one who will be his wife there is a proven and existing dimension of attraction and sexual desire, and even more so in the situation of the marriage proposal in which it is actually announced that this dimension will come to fruition. (In general, it is difficult to describe a person who hugs and kisses the choice of his heart and does not feel closeness and intimacy – which also has a sexual dimension).
So even if Kirtva eases other women with a touch of politeness and the like (even if it is a hug and a kiss as in certain cultures), it is difficult to expand on this case

Opinions can be raised in all directions (and also argued about in all directions. Because his wife is a virgin in front of a regular virgin). You asked a halakhic question and received an answer.