NOTE. The Skanda Purāṇa as quoted by Śrī Madhvācārya in his comment to Śrīmad-Bhāgavatam 9.10.11 explicitly notes that Lord Rāma only appeared to be distressed or frightened and that He is internally ever-blissful in full knowledge:

nitya-pūrṇa-sukha-jñāna-svarūpo ’sau yato vibhuḥ
ato ’sya rāma ity ākhyā tasya duḥkhaṁ kuto ’ṇv api

tathāpi loka-śikṣārtham aduḥkho duḥkhavartivat
antarhitāṁ loka-dṛṣṭyā sītām āsīt smarann iva

“Because the Almighty Lord has the nature of eternal and complete bliss and knowledge, His name is Rāma. Where is the question of Him experiencing even slight distress? Still, in order to teach the world, He who is devoid of distress appeared to become distressed while remembering Sītā when she had disappeared from worldly vision.”

In the Rāmāyaṇa, the Supreme Lord now begins to act like a human being, like in a dramatic performance. Whenever the Supreme Personality of Godhead incarnates in this world, He behaves in this manner as noted in Śrīmad-Bhāgavatam 1.3.37:

na cāsya kaścin nipuṇena dhātur
avaiti jantuḥ kumanīṣa ūtīḥ
nāmāni rūpāṇi mano-vacobhiḥ
santanvato naṭa-caryām ivājñaḥ

“The foolish with a poor fund of knowledge cannot know the transcendental nature of the forms, names and activities of the Lord, who is playing like an actor in a drama. Nor can they express such things, neither in their speculations nor in their words.”