Gaudapada makes it clear throughout his Mandukya-Karika that the ‘world is Brahman’ (he never uses this phrase as far as I recollect) only in the sense that the dream is the dreamer. It has no other reality – however nuanced by the word “relative”. For the jnani, both Gaudapada and Sankara write, this dream world is to be discarded, such that there is no further compulsion to action.
MK2.4. As the dream objects are unreal in a dream, so also, because of that very reason, the objects in the waking state are unreal. But objects (in the dream state) differ because of existence inside (the body) and because of contraction (in the dream).
MK2.31. Just as dream and magic are seen to be unreal, or as is a city in the sky, so also is this whole universe known to be unreal from the Upanisads by the wise.
MK2.33. This Self is imagined to be the unreal things and also to be non-dual; and these perceived things are also imagined on the nondual Self. Therefore non-duality is auspicious.
Sankara’s bhasya: In (such illusions as) “This is a snake”, “This is a stick”, “this is a streak of water”, etc. the very thing called rope is imagined to be such unreal things as a snake, a streak of water, etc. and also as the one real thing the rope; similarly, the Self is imagined to be such multifarious unreal things as Prana etc. which do not exist. But this is not done from the standpoint of reality, for nothing can be perceived by anybody unless the mind is active, nor can the Self have any movement. And things, perceivable to the unsteady mind alone, cannot be imagined to subsist in reality .
 Swami-G notes: “Diversity perceived on the motionless Self cannot be fancied to have real existence” is the interpretation according to Ananda Giri who takes “motionless” as the synonym of pracalita, that in which motion is absent.
MK3.10. The aggregates (of bodies and senses) are all created like dream by the Maya of the Self. Be it a question of superiority or equality of all, there is no logical ground to prove their existence.
MK3.24. Since it is stated (in the Vedas),“There is no diversity here,” and “The Lord, on account of Maya, (is perceived as manifold)”, “(the Self) without being born (appears to be born in various ways)”, it follows that He is born on account of Maya alone.
Sankara: Therefore creation, that has been imagined as a help to the comprehension of non-duality, is as unreal as the interlogue of Prana (vide Karika, III. 15); for this creation is referred to by the word Mitya, indicative of unreal things,
MK3.31. All this that there is—together with all that moves or does not move —is perceived by the mind (and therefore all this is but the mind); for when the mind ceases to be the mind, duality is no longer perceived.
Sankara: For duality endures so long as the mind does, and duality disappears with the disappearance of the mind. For when the mind ceases to be the mind, when, like the illusory snake disappearing in the rope, the mind’s activity stops through the practice of discriminating insight and renunciation, or when the mind gets absorbed in the state of sleep; duality is not perceived. From this non-existence is proved the unreality of duality. This is the purport. How does the mind cease to be the mind? This is being answered:
MK3.32. When, following the instruction of scriptures and the teacher, the mind ceases to think as a consequence of the realisation of the Truth that is the Self, then the mind attains the state of not being the mind; in the absence of things to be perceived, it becomes a non-perceiver.
Sankara: When as a consequence of that, there remains nothing to be thought of, and the mind does not think, as fire does not burn in the absence of combustible things; then, at that time it attains the state of ceasing to be the mind. In the absence of things to be perceived that mind becomes free from all illusion of perceptions. This is the idea.
MK3.33 bhasya Sankara: It has been said that when the mind is divested of ideation by virtue of the realisation of the Truth that is Brahman, and when there is an absence of external objects (of perception), it becomes tranquil, controlled, and withdrawn like fire that has no fuel. And it has further been said that when the mind thus ceases to be the mind, duality also disappears.
Sankara’s Brahma Sutra Bhasya
Thereafter, this thread can be picked up in Sankara’s Brahma Sutra Bhasya
1.1.4. In the case of an enlightened man there is a total absence of any connection with any impulsion to work. Hence a man who has realized his own identity with Brahman cannot continue to have the worldly state just as before, whereas the man who continues to have the worldly state just as before has not realized his identity with Brahman.
1.2.12. For these states of being an agent and experiencer are fancied on the soul and the mind, owing to a non-discrimination between their natures. In reality these are possible in neither of them; for the mind is insentient and the soul is changeless. This is all the more impossible in the mind, it being a creation of ignorance. In support of this here is a Vedic text: “Because when there is difference, as it were, then one sees another” (Br. IV. v. 15), where it is shown that dealings based on agentship etc. can be possible only within the range of ignorance in the same sense as it is possible to deal with elephants etc. present in a dream. And by the text, “But when to the knower of Brahman everything has become the Self, then what should one see and through what?” (ibid.), are denied for the discriminating man such dealings based on agentship etc.
1.3.1. From the appositional use (asserting Brahman’s identity with all) in, “All is Brahman” (Ch. III. xiv. 1), the doubt may arise that just as a tree is a composite entity, comprising as it does the branches, trunk, and roots, so also the Self is variegated and possessed of diverse tastes. In order to obviate that doubt, the text declares with emphasis: “Know that Self alone that is one without a second” (Mu. II. ii. 5). The idea expressed is this: The Self is not to be cognized as a heterogeneous thing comprising the manifold created universe . . . As for the use of “all” and “Brahman” in apposition in the text, “All this is (but) Brahman” (Ch. III. xiv. 1), it is meant for the elimination of the universe, and not for proving heterogeneity (in Brahman).
As to whether the jiva / world disappears on enlightenment, this is addressed head-on by Sankara:
BSB 4.1.3 The criticism is also unfounded that no one will be left over to practise the Vedantic path and that direct perception etc. will be outraged. For the transmigratory state is conceded before enlightenment, and the activities like perception are confined within that state only, because texts as this, “But when to the knower of Brahman everything has become the Self, then what should one see and through what?” (Br. II. iv. 14), point out the absence of perception etc. in the state of enlightenment.
Opponent: In the absence of perception etc. the Vedas also will cease to exist.
Vedantin: That is no defect, since that position is admitted by us.
To end, Vyasa himself in BS3.4.16 states: “Moreover from knowledge comes the destruction of the whole world”.
Sankara comments: Moreover, the scriptures declare that the whole world of manifestation, which consists of actions, instruments, and results, bestowing the necessary qualification for work, and which is a creation of ignorance, is destroyed root and branch by knowledge, as stated in, “But when to the knower of Brahman everything has become the Self, then what should one smell and through what?” (Br. II. iv. 14), and so on.
So no, the body-mind-world is not Brahman. And the jnani has no more relation to a non-existent body, mind or world, all imagined through ignorance. In fact there is no one to self-identify as a jnani. This is the depth of Gaudapada’s ajata vada:
MK 2.32 There is no dissolution, no origination [NO WORLD], none in bondage, none striving or aspiring for salvation [NO JIVA], and none liberated [NO JNANI]. This is the highest truth.
This is not a knowledge to be conceptualised by the mind; because the mind itself is borne of ignorance. Hence as discussed above, it too is discarded (“ceases thinking”) along with the body (‘as a snake sloughs its skin’), and there is no more desire or fear or agency.