But according to advaita, the paramatma IS the jivatman
There is never a plane of awareness in which the real , the illusion and the medium of illusion, all exist simultaneously.(contrasting to any analogy)
A treatise Tirumandhiram 2290 (by a well-known Rishi(of yore)Tirumoolar) explains the spiritual perfection as
Marathai Maraithathu Mamatha
Marathil Marainthathu Mamatha
Parathai Maraithathu Parmuthal
Parathil Marainthathu Parmuthal
Mara - Wood,
Para- Brahman, Bhootha-Pancha
An enraged wooden elephant, scares a child so long as, its not perceived to be all wood, akin to Jnanis realization that it's all Brahman , not so long as its all seen as Panchabhoothas
This can be translated to the dreamers analogy,(that only upon awakening ,the dream is an illusion,not so long as it is experienced). (another analogy)
Cognizing Paramatman and Jivatman as One is with reference to an awakened plane of awareness, in which there is no illusion.,otherwise undeniable plurality persist .
Also being an actionless entity why would the paramatma experience or feel the world
Drg Drishya Viveka(Advaita Prakarana grantha) shloka 7
chaayaa ahamkaarayoh aikyam tapta ayah-pindavat matam; tat ahamkaara taadaatmyaat dehah chetanataam agaat.
In the opinion of the wise, the identity of the reflection (of Consciousness) and of ego is like the identity of the fire and the (heated)iron ball. The body having been identified with the ego (which has already identified itself with the reflection of Consciousness) passes for a conscious entity, (Translation Swami Nikhilananda)
Here ayah-pindavat (also see Atma bodha ) is the typical example of mutual superimposition (anyonya adhyasa),where the shapeless fire takes the shape of iron ball , and the non-hot iron ball takes the heat of the fire, (known as taadaatmyaat ) hence creating the apparent appearance of sentiency ,propogating it to the body , causing an action to be made and thought to be formed, the karta , bhokta of samsaric experience.
Here in chapter 13 of BG, kshetram and kshetrajna (field and the knower of the field) bears ayah-pindavat mutual superimposition as explained above.
If paramatma is actionless and simply remains as a witness is reiterated in BG9.29
and is also cited in Br.Up.4.3.15
Swami Madhusudhana Saraswatis commentary on 13.22 Translation by Swami Gambirananda
(the Purusa) is the anumantā, Permitter. Though Himself inactive in the midst of the activities of the body and organs, He still seems to be active because, by His mere prox-
imity, He is favourable to them. Hence He is the anumantā. Or
the Purusa is the anumantā because, even though He is their
Witness, He never prevents the body, organs, etc. when they are
engaged in their own activities-as is said in the Sruti, (He is) the witness and bestower of intelligence (sv.6.11)
-the sustainer and nourisher,
through His own existence and self-effulgence, of body, organs,
mind and intellect, which form an aggregate and are endowed
with assemblance of Consciousness.
He is the bhoktā, Experiencer, without being affected in any way, in the sense that He illumines, through His own nature as Consciousness, the intellect's experiences in the form of happiness, sorrow and delusion.(in otherwords experience is not possible without mutual superimposition)
(In addition to HH Shankaracharya s commentary cited by @Student)