Merriam-webster describes reactionism as of, pertaining to, marked by, or favoring reaction, especially extreme conservatism or rightism in politics; opposing political or social change. And according to wikipedia, a reactionary may be described as:
In political science, a reactionary is a person or entity holding political views that favour a return to the status quo ante, the previous political state of society, which they believe possessed characteristics that are negatively absent from the contemporary status quo of a society.
The latter part of the Wikipedia definition reminds me of a slogan that was popular in the 2016 United States Presidential Election campaign of Donald Trump, Make America Great Again, but I am not aware of this campaign or its supporters self-describing as reactionary.
Rather, I seem to have encountered reactionary and reaction only as a description by opponents, in particular opponents on the far left, such as in the book titles Between Anarchist Rebellion and Fascist Reaction or The shipwrecked mind: on political reaction. I've also heard the term used by conservatives to describe others on "their side" of politics, in the sense of, "that opinion/group is not/no longer conservative, it has become reactionary", after a previously centrist or centre-right party or group has shifted toward the political right, or is perceived to have done such.
As a label, are there any political parties or groups that self-describe as reactionary? The Reactionary Party of Reactistan? The Movement for a Reaction? Reactionaries United?