I disagree. Look at the way we talk about it, "the covid", "covid did this", etc. It absolutely would have worked as an enemy to declare war on and I don't think the vast majority of people would consider it trump's fault if he just got out ahead of it.
Imagine a world where he didn't do trumpy things and instead did things like talking about how this is a national, world wide foe we all need to work together to defeat, I know it's hard, we'll all make sacrifices, but we're the nation that beat the nazis and went to the moon, we can win this war on covid. For further details here are my science advisors talking about the latest info on counter measures.
Obviously this is imagining a world where trump isn't trump, but I very much believe obama/clinton/bush/etc would have been re-elected.
Keep in mind that we also have a strong tendency to re-elect the incumbent anyways and covid is an amazing opportunity to blame all your previous fuck ups on this new "totally unforseeable/preventable disease cataclysm!"
If he had a chance of being re-elected, it was certainly dead after his attempts at dealing with covid.
In the case of Bush in the 2004 election, at that time they were pushing the story that Iraq had been developing WMDs; that was the initial justification for the invasion. Obviously false in hindsight, but at the time people were still pretty raw about 9/11, so critical thinking was in short supply, but--most importantly--it provided an enemy to focus on.
In the case of covid there was no comparable enemy. "Declaring war" on a virus would not have anywhere near the same impact as using the military to actually wage war on another country.