It is difficult to find estimated dates for the completion of renovations on these two sites. Does anyone have such information?
I tried to search it out and unfortunately could only find that the Blue Mosque is still open despite the restoration. I could not find when the closed parts of Topkapi Palace would reopen (https://topkapisarayi.gov.tr/en/visit-information). The palace is so huge that it's still worth going to, even if some sections are closed. Also, even though the Blue Mosque is the best known, there are countless of other interesting mosques that I would visit for comparison sake. You can find all of them on Wikipedia (just search Istanbul Mosques). My favorites are Rustem Pasa and Sulemanyie.
No one knows when the renovations on the Blue Mosque will be finished, Most of these types of renovations in Istanbul take at least two years. You should still go to the Blue Mosque though. It is free (they like donations though). The Süleymaniye Mosque was recently restored/renovated and looks gorgeous! The Süleymaniye Mosque is 200 years older than the Blue Mosque. Süleymaniye Mosque is on top of a hill, so there is a great view of the city from the garden behind the Mosque.