Is it true that Al-Aqsa Mosque is the Qibli Mosque?

The Qibli Mosque is part of Al-Aqsa Mosque, located in the direction of the Qibla, and it is the main prayer hall built by Omar ibn al-Khattab, may Allah be pleased with him. Sheikh al-Islam Ibn Taymiyyah mentioned that Al-Aqsa Mosque is the name for the entire mosque built by Solomon, peace be upon him.

Most exegetes believe that Al-Aqsa Mosque in the verse (سُبْحَانَ الَّذِي أَسْرَى بِعَبْدِهِ لَيْلًا مِنَ الْمَسْجِدِ الْحَرَامِ إِلَى الْمَسْجِدِ الْأَقْصَى), "Exalted is He who took His Servant by night from al-Masjid al-Haram to al-Masjid al-Aqsa," refers to Bayt al-Maqdis (Jerusalem). Al-Aqsa Mosque encompasses the entire Noble Sanctuary (Haram al-Sharif), including the Dome of the Rock and the Qibli Mosque, and everything within its walls. Its area is approximately 144 dunams, occupying about one-sixth of the Old City's area.