We were never at war with "Syria" under Obama. We were at war with terrorist groups inside Syria, including ISIS, who it has been argued was a proper target under both the 2001 and 2002 AUMFs. The 2001 AUMF is not a great argument for the reasons you mention.
The 2002 AUMF is probably a better argument, since ISIS was operating in Iraq, although it is more difficult to argue that it supported the portion of the war against ISIS carried on inside of Syria. Of note, Trump continued this war against ISIS in Syria without getting an AUMF of his own. So any problems Obama had with using the 2002 AUMF in this way can be attributed to Trump as well.
Between Obama and Trump, Trump is the only one who famously shot missiles at the Syrian government *directly* in retaliation for their use of chemical weapons. https://en.wikipedia.org/wiki/2017_Shayrat_missile_strike. He probably should have gotten an AUMF to do that.
Indeed, we were at war with Libya, and yes, Obama should have gotten an AUMF for that.
I don't know where you're getting this notion that I have supported every bombing decision Obama has made. I can criticize him, and I can criticize Trump, and I can criticize even Congress for not properly doing its job and insisting on an AUMF every time it's needed.