A 32-year-old man from Delhi presents with a 3-week history of fever, productive cough, and dyspnea. He is known to be HIV-positive with a CD4 count of 85 cells/μL (measured 2 weeks ago). On examination, he is febrile (38.5°C), tachypneic (RR 28/min), and has bilateral fine crackles on auscultation. Chest X-ray shows bilateral interstitial infiltrates with a ground-glass appearance. Arterial blood gas shows PaO₂ 65 mmHg on room air. LDH is elevated at 520 U/L. What is the most likely diagnosis?