True for (Soul as paramatma as one supersoul residing in hearts of all being) and Not true for (Another as jivatma residing in hearts of each being as unique to that being) there are 2 souls in each living being (even tough there can be many jivas in the same body but one primary jiva is the enjoyer of fruits) i.e. chetana as described as dvsuparana in
Mandukya Upanishad 3.1:1
द्वा सुपर्णा सयुजा सखाया समानं वृक्षं परिषस्वजाते।
तयोरन्य: पिप्पलं स्वाद्वत्त्यनश्नन्नन्यो अभिचाकशीति॥
समाने वृक्षे पुरुषों निमग्नोऽनाशया शोचति मुह्यमान:।
जुष्टं यदा पश्यत्यन्यमीशमस्य महिमानमिति वीतशोक:॥
यदा पश्य: पश्यते रुक्मवर्णं कर्तारमीशं पुरुषं ब्रह्मयोनिम्।
तदा विद्वान्पुण्यपापे विधूय निरंजन: परमं साम्यमुपैति॥
Dwa Suparna Sayuja Sakhaya Samanam Vriksam Pariswajate
Tayor anyah pippalam swadu atti, anashnan anyo abhijakashiti. - Mundaka Upanishad 3.1:1
Samane vrikshe purusho nimagno 'nishaya shocati muhyamanah
Jushtam yada pashyati anyam isham asya mahimanam iti vita-shokah - Mundaka Upanishad 3.1:2
Yada pashyah pashyate rukma-varnam kartaram isham purusham brahma-yonim
Tada vidvan punya-pape vidhuya niranjanah paramam samyam upaiti - Mundaka Upanishad 3.1:3
Meaning in English:
Two birds living together, each the friend of the other, perch upon the same tree
Of these two, one eats the fruits of the tree, but the other simply looks on without eating.
Although the two birds are on the same tree, the eating bird is fully engrossed with anxiety and moroseness.
If in some way or other he turns his face to his friend who is the Lord, at once the suffering bird becomes free of all anxieties
One who sees the golden colored bird, the Lord, the actor, who is the source of the Supreme Brahman, is liberated.
Such a person becomes wise. He becomes free of both pious and sinful karmic reactions. He becomes pure. He attains a spiritual form like that of the Lord Himself.