I should say off the bat that most of the books that handle the post-Soviet period specifically cover Russia (it's half the population and 3/4 the area of the former USSR, and is its legal successor state after all). I mentioned some primer sources on post-Soviet Russia here and provide some additional ones on the end of the Soviet Union if that's of interest. A lot of this also comes from historians writing about post-Soviet Russia also being historians of the Soviet Union, and having at least a working knowledge of Russian and of the now-Russian archives.

In general, while there are some histories that touch a bit on the paths that other former Soviet republics have followed post-1991, I actually don't know off the top of my head of a single narrative history that covers them all, and I'm not really sure if such a book could do them all justice - Estonia is a far cry from Tajikistan, it must be said. Usually the histories that you get about post Soviet states tend to be regional, if not focused on specific countries. So in the case of Armenia I'll pass the buck to someone who is more knowledgeable of the Caucasus (u/kaisermatias?).

As for histories of Uzbekistan, especially around post-Soviet state building, I'm on a little firmer territory.

You'd probably want to start by consulting Edward Allsworth's The Modern Uzbeks - this was originally written in 1987, so he only touches on the beginning of the transition period, but it's a very comprehensive thematic history of the Uzbek people and developments in what is now Uzbekistan.

Adeeb Khalid is the go-to expert on the history of Islam in modern Central Asia, and he has written three books that cover that topic and are focused on Uzbekistan: The Politics of Muslim Cultural Reform: Jadidism in Central Asia covers the early 20th century, Making Uzbekistan: Nation, Empire, and Revolution in the Early USSR covers the early Soviet period, and Islam after Communism: Religion and Politics in Central Asia covers the late Soviet period and history through independence to roughly 2000 or so.

Olivier Roy's The New Central Asia: Geopolitics and the Creation of Nations is worth a read. Roy was a French diplomat in Tajikistan in the 1990s, and this book is largely primarily on Tajikistan (but Uzbekistan plays a major role) and also more on the sociology of the region than just a straight-up political history. Feel free to skip his last chapter on conclusions since they're woefully out of date.

Svat Soucek's History of Inner Asia covers a much, much broader area and time period (basically the former Soviet Central Asia plus Afghanistan, Mongolia, and Xinjiang for all of recorded history), but has some pretty solid info on the post-1991 period.

You also might want to check out Alexander Cooley and John Heathershaw's Dictators Without Borders: Power and Money in Central Asia has a chapter on each Central Asian country, highlighting a major international corruption scandal in each. Strictly speaking they are political scientists and not historians, and are not covering history of the countries per se, but this book does a good job of situating what high-level corruption in the region looked like post 1991, and how international institutions both aided it and were abused by it.

There are some other books that are on my to-do list and that I am therefore regrettably not personally acquainted with yet, that you might want to check out: Pamela Blackmon's In the Shadow of Russia: Reform in Kazakhstan and Uzbekistan, Dilip Hiro's Inside Central Asia: A Political and Cultural History of Uzbekistan, Turkmenistan, Kazakhstan, Kyrgyzstan, Tajikistan, Turkey, and Iran, and Pauline Jones Luong's (as editor): The Transformation of Central Asia : States and Societies From Soviet Rule to Independence

/u/Kochevnik81 is right, I can contribute a bit for Armenia.

Most of the books on post-Soviet Armenia are heavily slanted towards the Nagorno-Karabakh conflict, as it has obviously had a huge impact on the country. However most of the literature is written by people from the Armenian diaspora, so I'm cautious about their views on it. Thomas de Waal's Black Garden: Armenia and Azerbaijan Through Peace and War is probably the best, most neutral book on the war, and looks at developments in each country as well, so would suggest looking at that.

And I both own Dilip Hiro's Inside Central Asia and have read it, and found it a great introductory text on the region. It does a great job and explaining the modern developments of each country up to publication, as well as some background on them as well. I'd also recommend another book by Alexander Cooley aside from Dictators Without Borders: Great Games, Local Rules: The New Great Power Contest in Central Asia, which looks at how the US, Russia, and China are all vying for influence in the region, and how that impacts each place. Uzbekistan has taken a major role in that, so it features quite prominently in the book.