NOTE. Why does Kausalyā-devī worship the devas here? Isn’t worship of the devas and the like severely criticized in the Bhagavad-gītā for those who want immediate liberation from material existence and hence it is obviously useless for pure devotees of the Supreme Personality of Godhead?

That is true, for Prabhupāda writes in his purport to Bhagavad-gītā (4.12):

Foolish people (hṛta-jñānāḥ) worship the demigods because they want immediate results. They get the results, but do not know that results so obtained are temporary and are meant for less intelligent persons. The intelligent person is in Kṛṣṇa consciousness, and he has no need to worship the paltry demigods for some immediate, temporary benefit. The demigods of this material world, as well as their worshipers, will vanish with the annihilation of this material world. The boons of the demigods are material and temporary. Both the material worlds and their inhabitants, including the demigods and their worshipers, are bubbles in the cosmic ocean. In this world, however, human society is mad after temporary things such as the material opulence of possessing land, family and enjoyable paraphernalia. To achieve such temporary things, people worship the demigods or powerful men in human society. If a man gets some ministership in the government by worshiping a political leader, he considers that he has achieved a great boon. All of them are therefore kowtowing to the so-called leaders or “big guns” in order to achieve temporary boons,  and they indeed achieve such things. Such foolish men are not interested in Kṛṣṇa consciousness for the permanent solution to the hardships of material existence. They are all after sense enjoyment, and to get a little facility for sense enjoyment they are attracted to worshiping empowered living entities known as demigods.

However, pure Vaiṣṇavas sometimes worship demigods and demigoddesses with the exclusive desire to attain service to the Supreme Lord or in service to Him:

The Vaiṣṇavas generally do not worship any demigods. Śrīla Narottama dāsa Ṭhākura has strictly forbidden all worship of the demigods for anyone who wants to advance in pure devotional service. Yet the gopīs, who are beyond compare in their affection for Kṛṣṇa, were seen to worship Durgā. The worshipers of demigods sometimes mention that the gopīs worshiped Goddess Durgā, but we must understand the purpose of the gopīs. Generally, people worship Goddess Durgā for some material benediction. Here, the gopīs prayed to the goddess to become wives of Lord Kṛṣṇa. The purport is that if Kṛṣṇa is the center of activity, a devotee can adopt any means to achieve that goal. (Kṛṣṇa, Chapter 22)

The gopīs worshiped Goddess Kātyāyanī to get Kṛṣṇa as their husband; similarly Rukmiṇī was thinking of the various types of demigods not for material benefit but in respect to Kṛṣṇa. Praying to the demigods to achieve the favor of Kṛṣṇa is not irregular, and Rukmiṇī was fully absorbed in thoughts of Kṛṣṇa. (Kṛṣṇa, Chapter 53)