I know Congress needs to be involved to actually declare war, but there have been a number of times where something was kicked off by presidential authority alone.
If Biden wanted to, could he start a conflict against Russia without congressional approval. If not, what approval would he need? If so, what would be the theoretical limitations to his power and military authority?
I am already assuming people would want some definition of what “conflict” would mean in this hypothetical scenario. So let’s say it means Biden authorized US troops at the Ukrainian border and had them launching shells into Russia.
Only Congress can officially declare war.
Right and when was the last time that process was actually followed?
A declaration of war does not need to be given.
Since 1973, sustained military operations have required Congress’ approval. A declaration of war is not needed, but the process of Congress voting to authorize military forceis. That is essentially the same process with a few words swapped out. That process has been followed.
Now, if you are in the mood to look for issues, look at the 2001 AUMF passed by Congress. It gave a blank check to conduct military operations against “those responsible for the 9/11 attacks”. Given enough lawyers and determination, that can be read very, very broadly. That AUMF is still being cited for operations. The process has been followed to the tee, and Congressed did indeed sign off on it, but that is an example of a broad and open ended power being given away by one branch of government to another.