What is the deeper meaning of the teaching that the seal of Hash-m is truth?

Rashi (Shabbos 55a dh Chosmo): The word Emes (א-מ-ת) is composed of the first, middle, and last letters of the Alef-Beis, alluding to Hash-m, Who declares (Yeshayah 48:12), "I am first, and I am also last". This teaches that Hash-m's truth encompasses all of reality, from beginning to end. As the One who creates and directs all existence, Hash-m alone defines absolute truth. Accordingly, the Gemara describes truth as His 'seal', the imprint of His presence upon creation. (An interesting allusion attributed to the Vilna Gaon is that Rashi's commentary on the Torah, accepted to have been written with Ruach HaKodesh - Divine inspiration, likewise begins with an Alef and ends with a Tav, subtly reflecting this same theme of Emes.)

Chofetz Chaim Al HaTorah (Bamidbar 23:10 - Maasei L'Melech): The Gemara's statement that 'the seal of Hash-m is truth' can be understood through the nature of a seal: its letters are engraved in reverse and only become readable once an impression is made. So too, the truth of Hash-m in the world is often not immediately perceptible in its source; it is only when it becomes 'imprinted' in reality, through events in the physical world, that it becomes recognizable to most people. However, there are select individuals who are able to 'read' the seal itself - to perceive the Divine truth at its source, even before it is expressed in the physical world.

Why was the Yetzer Hara in the Holy of Holies?

Toras Chaim (brought in Eitz Yosef Yoma 69b): The creation of the world parallels the creation of man, which is why man is called an Olam Katan (a miniature world). Just as the Yetzer HaRa first resides within a person at his heart - the body's central point and root - and from there spreads throughout the rest of the body, so too the Yetzer HaRa has its place within the world at its central point and root: the Even Shesiyah, the foundation stone from which the world was created, located in the Kodesh HaKodashim. From there, it extends throughout the entire world.

Michtav Me'Eliyahu (4:174): The desire for Avodah Zara originally came from a deep spiritual drive for closeness to Hash-m. The fiery lion reflected the strength of that drive. Avodah Zarah resulted when this powerful force was misdirected and corrupted away from true Avodas Hash-m.

Rav Chaim Kanievski #1(quoted in Sefer Aryeh Sha'ag 795): It is to show that the Yetzer HaRa can enter even there.

Rav Chaim Kanievski #2 (ibid): When it is brought there, it enters. (Perhaps he means that the Yetzer HaRa gets into the Kodesh HaKodashim because the sins of Klal Yisrael spiritually bring its influence into there.)

What is the significance of the different comparisons in clinging to Baal Peor and (lehavdil) clinging to Hash-m given by Rav and in the Braisa (Rav - lid/date-palms; Braisa - bracelet/truly attached)?

Ein Eliyahu: This aligns with the two opinions in Berachos 34b as to whether a Baal Teshuva (one who sinned and repented) or a Tzadik Gamur (one who never sinned) is greater. According to Rav, who holds a Tzadik Gamur is greater, after the sin of the Golden Calf and their Teshuva, Bnei Yisrael were still not at the level of a Tzadik Gamur. When they later sinned again with Baal Peor, their attachment to idolatry became a Chazakah, and was therefore compared to a lid tightly covering its vessel. Even after Teshuva, their attachment to Hash-m is described as like two date palms - close but still side-by-side. In contrast, the Braisa follows the view that a Baal Teshuva (one who sinned and repented) is greater than a Tzadik Gamur (one who never sinned). Therefore, after the sin of the Golden Calf and their Teshuva, Bnei Yisrael became very firmly attached to Hash-m. However, by later sinning with Baal Peor, they weakened that attachment, so they were then connected to Hash-m only like a bracelet - very close, but still external. After they again did Teshuva, they became completely attached to Hash-m.

Maharsha: The Braisa contrasts the difference in the degree of connection that Yisrael had. Since they served Baal Peor for ulterior motives (as they were drawn to the Moabite women), their connection was weaker and compared to a bracelet. In contrast, they served Hash-m out of genuine devotion, so their attachment to Him was complete and far more deeply rooted.

Meshech Chochma (Bamidbar 25:5): The Baraisa's contrasting comparisons reflect the fundamentally different nature of these two forms of attachment. Those who worshipped Baal Peor were attached only like a bracelet worn externally, whereas those who were clinging to Hash-m were truly and intrinsically bound to Hash-m. (This is reinforced by the Torah's choice of prepositions: they were 'Nitzmadim L'Baal Peor' but 'Deveikim BaHashem'. Torah Temimah there). This is especially fitting because, although idolatry normally stems from a person's higher spiritual faculties, the worship of Baal Peor was motivated by physical desire. Their attachment to the idol was therefore only external, while those who remained clinging to Hash-m possessed an inner spiritual bond that enabled them to overcome those physical temptations.

Maharal of Prague (Chiddushei Agados): Yisrael's vulnerability to Baal Peor occurs when they lose their intrinsic state of spiritual completeness (Shleimus). In a state of lack or deficiency, a person naturally gravitates toward an equally deficient and empty reality, because "the deficient craves the deficient". Rav views this attachment as a tightly sealed lid on a jar, meaning they become locked into this state of lack. The Beraisa, however, compares it to a woman wearing bracelets to show that this connection is purely external, since idolatry stands entirely outside the true order of existence. When it comes to Hash-m, our bond is natural and essential. Rav compares it to two palm branches that stay distinct but tightly bound together, while the Braisa says it is an absolute attachment, just like a tree locked into its own roots.