In the hadith you quoted, the word "house" is a reference to Jannah and associated places of intercession, not to a physical house for Allah.
In Fat'h Al-Bari (Arabic: فتح الباري شرح صحيح البخاري) by Ibn Hajar al-Asqalani (Arabic: أحمد بن علي بن حجر العسقلاني), the commentary on this hadith explains this phrase:
وقوله « فأستأذن على ربي في داره فيؤذن لي عليه » قال الخطابي هذا يوهم المكان والله منزه عن ذلك، وإنما معناه في داره الذي اتخذها لأوليائه وهي الجنة وهي دار السلام، وأضيفت إليه إضافة تشريف مثل بيت الله وحرم الله
— NOTE: My own translation, so treat with care:
And his saying [in Sahih al-Bukhari » Book of Oneness » Hadith 7440]: "and I will ask my Lord's permission to enter His House and then I will be permitted", Al-Khattabi said this may insinuate a place, and Allah is exalted from that. Rather, this means a house that Allah has ordained for his guardians, namely Jannah, which is the house of peace. The attribution to Allah is a form of honoring the place, as in the case of calling [Al-Ka'aba] the house of Allah, or the sanctity of Allah.
This is a common phrase in the Arabic language — as well as other languages — to elevate the stance of a place. Calling Al-Ka'aba the House of Allah does not refer to it as a physical lodging anymore than Christians calling a church the House of God. This is also demonstrated in multiple verses in the Qur'an:
وَاللَّهُ يَدْعُو إِلَىٰ دَارِ السَّلَامِ وَيَهْدِي مَن يَشَاءُ إِلَىٰ صِرَاطٍ مُّسْتَقِيمٍ
And Allah invites to the Home of Peace and guides whom He wills to a straight path
— Qur'an 10:25
Similarly, Al-An'am 6:127 and Fussilat 41:28 use the word house in a similar fashion. Ibn Al-Qayyim and 'Abdul-Haq Al-Eshbeeli said that the reference in this hadith is to the places of shafa'ah (intercession) — Refer to Ijtima' Al-Juyush Al-Islamiyyah (Arabic: اجتماع الجيوش الإسلامية
) and Ma'arij Al- Qubool (Arabic: معارج القبول بشرح سلم الوصول إلى علم الأصول
Having said that, from a hadith perspective, this particular phrase of "and I will ask my Lord's permission to enter His House" was narrated only through the chain of Hammam Ibn Yahya (Arabic: همام بن يحيى) as per Ibn Hajar in the commentary linked above. In Sahih Al-Bukhari, this hadith was also narrated through three different chains (Hisham through Qatada in Sahih al-Bukhari » Book of Oneness » Hadith 7410 and Sahih al-Bukhari » Prophetic Commentary on the Qur'an » Hadith 4476, Abu-'Uwana through Qatada in Sahih al-Bukhari » Book of To make the Heart Tender » Hadith 6565, and through Ma'bad bin Hilal Al-'Anzi in Sahih al-Bukhari » Book of Oneness » Hadith 7510) that do not have the phrase "and I will ask my Lord's permission to enter His House".
In other books of hadith (Sahih Muslim » The Book of Faith » Hadith 193 a, Sunan Ibn Majah » Zuhd » Hadith 4454, and Jami' at-Tirmidhi » Chapters on Tafsir » Hadith 3441, among others), said phrase is also missing from the verse of the hadith.