With Palestine vs Israel I would tend to call it a war since Palestine's own country was taken and it is occupied by different artifically created country, so I would say it is two countries at war.
Think if Russia today arms an anti-democracy militia in Canada in order to destabilise USA. Any subsequent invasion of Canada by US would be a natural order of power play.
The US did not arm the Islamists in order to destabilize Russia, just a Russian client. In response, Russia invaded and removed the client government - the very government that the Islamists were trying to remove.
If Russia today armed an anti-democracy militia in Canada, would the US invade Canada? No (at least, any previous administration would not). We would share intel, help cut off the flow of arms, maybe even do a joint operation against the militia. But conquer Canada? Why would we do that?
So your analogy is as flawed as your moral equivalence.
Insisting on dichotomy between attempting to destabilise a union or one of it's bordering states, a client/satellite state is clutching at the straws.
You overlook categorical differences where it matters and then makeup binary lines for nuanced and things that happen on a spectrum like destabilisation where it is convenient for you. That is lazy at best, or dishonest at worst.
> But conquer Canada? Why would we do that?
You seem to have no idea about US is conduct with it's allies throughout history where it comes to her interests priority. Henry Kissinger didn't say "It may be dangerous to be America's enemy, but to be America's friend is fatal." because he felt like it. It is a reflection of US's modus operandi. Liberia, Panama, Argentine Junta, Iraq, Iran, Iraqi Kurds of 70s, Peshmarga of 2020s, Nicaragua in 80s, endless examples.
The problem is not with the analogy, it is your lack of understanding of US's modus operandi and her historical conduct.