1849 Budapest became possible with the construction of the Chain Bridge finally connecting Buda and Pest. The first great growth spurt begings.
In 1867 the creation of the Dual Monarchy with Austria helped to put aside any uncertainity of war with Austria and bumped the income and status and growth of the nation.
1873 Buda, Pest, Obuda come together to form Budapest, again an increase in growth.
1896 millennium celebrating 1000 years of Magyar occupation in the region; ie the formation of Hungary. If someone asks you when some great building was constructed and you want to look smart, say it was constructed for the 1896 millennium. 50/50 chance you will be correct. The castle mentioned above was constructed as an exhibit.
Most of the apartment blocks/shops in Districts one generally visits as a tourist were constructed between 1890 and 1920. While the Millennium was instrumental in the building boom, the Treaty of Trianon put a real hamper on it.
Here is a tiny bit on the history on the Basilica
Begun in 1851 (first architect died midway through).
Dome collapsed in 1868,
1869 Second architect dies
Completed in 1905.
https://pestbuda.hu/en/cikk/20220623_the_dome_of_st_stephen_s_basilica_went_up_in_flames_75_years_ago#:~:text=During%20the%20World%20War%20II,on%20the%20north%20east%20side.