about how the russian empire fought a 30 year colonial war to conquer chechnya

I mean Russian Empire did tried to conquer entire Caucasus since like Peter the Great, and that surely do cause some resentment even today, but considering large part of the region remains in Russia that leave us with one or both of conclusions that: it's mostly irrational russophobia like in Poland or it's been stoked by foreign powers... again like in Poland so if you look at countries around Russia you would notice those that those versions are basically one and the same.

The second was a russian soldier’s (arkady babchenko) account of his nightmarish experiences during the 1st and 2nd wars that russia launched to retake chechnya

I didn't read that, but i would remain very careful about the source. There's a lot of antirussian propaganda being printed even in Russia (yay wonders of private publishing, Lenin and Zhdanov were right about it) and Chechen wars remain one of prime source of that (though Ukraine is replacing it because westerners can't even pretend they care for Chechens) since i don't deny they were hard and brutal.

This is what informed my opinion of the relationship between imperial/modern russia and chechnya being one of attempted subjugation

This is probably when you went incorrect. Russian Empire was, well, an empire which tried to conquer left and right, but back then the world and especially remote places like Chechenya weren't in the imperialist, let alone global imperialist phase of development meaning it was between Russia and Chechenya. In 1991 situation was entirely different though, Russia was a defeated country being plundered by victorious world hegemon and its own compradors but it still had the potential for resurgence. Standard US doctrine (and in fact every hegemonic doctrine since Assyrian Empire) uses places like Chechenya to destabilise regions, and it worked, looking at the wars. First Chechen war was probably a blunder, that could be solved better but it would also required better people at the helm of Russia, however even without the war it could as well turned into local ISIS considering who was in their govt and army and how they held power by sheer force of arms. but then look at what happened after war, Chechenya DID turned into local ISIS, so the 2nd war was in reality about the very same reason that intervention in Georgia in 2008 and SMO in 2022.

So could I please know the non-propaganda QRD of the situation?

This was from my own perspective as i observed the events, publications i have access to in Poland are junk, basically "evil Russia does evil because they are evil".

There was an anticommunist secessionist coup in chechnya as soon as the USSR dissolved.

This is actually even in main wiki article about Chechenya :) Though it was during, not after.

Also what were the reasons behind the 1st coup?

There was ton of fuckups during the destruction of USSR so i don't exactly remember, but likely the same as in other republics. Key point that led to 1st war is that Chechenya didn't legally seceded from USSR like other republics which did but declared independence unilaterally later, and not from USSR but from Russia, probably prompting Yeltsin govt to feel endangered that whatever left of USSR will further disintegrate. As we know they were wrong, Russia didn't further break up even though they lost that war, but the danger was real from that point of view, especially after feeling the embrace of shock therapy.