In general, classical Indian philosophers tend to define śarīra ‘body’ as a tool for experience (bhogasādhana). Thus, most philosophers state that plants only seem to have bodies because of our anthropomorphic tendencies, which make us believe that they function like us, whereas in fact plants cannot experience. By contrast, Veṅkaṭanātha in the Nyāyasiddhāñjana defines śarīra in the following way:
Therefore, this śarīra is of two types: permanent and impermanent. Among them, permanent are God’s body —consisting of auspicious substrates, namely substances with the three qualities, time and [individual] souls— and the intrinsic form of Garuḍa, the snake (Ananta), etc. belonging to permanent [deities]. The impermanent [body] is of two types: not made of karman and made of karman. The first one has the form of the primordial natura naturans (the prakṛti of Sāṅkhya), etc.* of God. In the same way, [an impermanent body not made of karman] assumes this or that form according to the wish of the liberated souls, such as Ananta and Garuḍa. Also the [body] made of karman is of two types: made out of one’s decision and karman and made out of karman alone. The first type belongs to great [souls] like the Muni Saubhari. The other one belongs to the other low [souls] (i.e., all normal human beings and the other conscious living beings). Moreover, the body in general is of two types, movable and unmovable. Wood (i.e., trees) and other [plants] and rocks and other [minerals] are unmovable. […] That there are souls also in rock-bodies is established through stories such as that of Ahalyā.
tad etat śarīraṃ dvividham —nityam anityañ ceti. tatra nityaṃ triguṇadravyakālajīvaśubhāśrayādyātmakam īśvaraśarīram; nityānāñ ca svābhāvikagaruḍabhujagādirūpam. anityañ ca dvividham —akarmakṛtaṃ karmakṛtañ ceti. prathamam īśvarasya mahadādirūpam. tathā anantagaruḍādīnāṃ muktānāñ ca icchākṛtatattadrūpam. karmakṛtam api dvividham. svasaṅkalpasahakṛtakarmakṛtaṃ kevalakarmakṛtañ ceti. pūrvaṃ mahatāṃ saubhariprabhṛtīnām. uttarañ ca anyeṣāṃ kṣudrāṇām. punaḥ śarīraṃ sāmānyato dvidhā jaṅgamam ajaṅgamañ ceti. kāṣṭhādīnāṃ śilādīnāñ ca ajaṅgamatvam eva. […] śilādiśarīriṇo ‘pi jīvā vidyante iti ahalyādivṛttāntaśravaṇāt siddham (Nyāyasiddhāñjana, pp. 174–176).
Thus, the deities have an intrinsic form which is permanent and can assume further impermanent ones at wish, not depending on karman.
As for rocks and stones, the rationale of their inclusion is the story of Ahalyā, who was transformed into a stone and then back into a woman, a fact which proves that a soul was present also while she was a stone. Her story is told, e.g., in the Rāmāyaṇa.
*The first commentary explains this ādi as referring to God’s emanations, the vyūhas, which are a typical mark of Pāñcarātra theology throughout its history.
Note the limitation in the precinct of application of karman, which seem to only determine one’s body and not one’s entire life. Further, why do you think Veṅkaṭanātha does not explain away Ahalyā’s story? What is he aiming at through the inclusion of stones?
On nature and sentience of plants in Classical Indian Philosophy, see this post and this one (in general) and this one (on Buddhist philosophy) and in general this label in my old blog. On Veṅkaṭanātha, see this label.