The Klingons seem to be targeting ships and the infrastructure for an interstellar nation, not the member planets.
At the early stages of the war, yes. But amusingly, it seems they aren't achieving much even against Starfleet's assets. The death toll from the very first clash seems to be exactly what Burnham's not-quite-cellmate accuses her of six months into the conflict, even though said accuser clearly is blaming the whole war on Burnham.
The average civilians life is largely unaffected, because this isn't Total War. The 8000 was all Starfleet, an organization made up of explorers and scientists, not hardened soldiers, and everyone in Starfleet knows someone who died.
Burnham's accuser would by default hold a different viewpoint yet agrees with the figures, erring in favor of Burnham if anything. Even to her, only the Starfleet dead appear to matter, giving all the more support to the interpretation that this is a war for Starfleet rather than for the Federation. And, incidentally, allowing Carol Marcus to think that Starfleet has "maintained peace" for a century as of the 2280s - by keeping all the wars in outer space!
maintain that Starfleet is losing the war. The low casualties can have many in universe explanations.
But we then need some other definition of "losing", such as territorial losses, and we never really hear of such. There are alarming Klingon intrusions into UFP space, but perhaps mirrored by Starfleet forays to restore the balance. There is no concern yet over dwindling resources or mention of a shortage of starships that would not be matched by similar shortage on the Klingon side. The ambiguous maps on the walls don't establish increasing or decreasing dominance for either player.
We would at a minimum need a character express the sentiment that Starfleet is losing, or perhaps winning; we instead get platitudes of good fighting going on and good people being lost, as if the war were a far less bloody version of the WWI stalemate.
Discovery's repeated success in battle is down to Mirror Lorca having more combat experience than anyone in Starfleet and how he was able to grab a mostly intact, but blooded, crew assembled by Captain Georgiou. A crew already used to dealing with an eccentric, even erratic First Officer, so they can still function under Lorca.
But even the fights
Discovery fight only start those six months into the war, and seem to be a handful, when enumerated at the start of "Choose Your Pain". They are also rather directly credited to the use of the spore drive. Basically, it seems that both sides sit in their WWI trenches (but don't kill millions in idiotic charges) while waiting for the penetrating tank to be invented - and Starfleet knows it has already invented the tank and now waits for it to be mass-produced, i.e. DASH installed aboard actual fighting ships. In the meantime, Klingons do nothing, lacking this all-important ability to deploy a "ghost".
Then comes Kol, and suddenly
his ships are ghosts, ambushing individual Starfleet vessels six to one and scoring easy victories when the victims have no warning and the only help that can arrive in time is the weakly armed (if determined) science vessel. And yet we get hardly a casualty added to the initial total, by the time of "Magic", and people seem to share a belief that Klingons just might call it quits if getting to publicly gut and eat Burnham, and everybody could go back home by Christmas.
And then, apparently, Kol manages to expand his power base by bribing a lot of Houses with cloaking capability, and suddenly those Houses begin competing in the categories of "Most Spectacular Massacring", "Most Glorious Looting", and "Most Harebrained Suicidal Strike Against Powerful Target". All result in casualties - but an indirect result would appear to be that territorial gains also finally enter the picture. Sure, when Klingons defeat a starbase with 80,000 people aboard, they apparently lose tens of thousands themselves, there only being a pitiful occupying force of less than 300 subsequently. But after a victory like this, the Klingons don't retreat; they become a presence, no matter how frail.
Might not be what Kol wanted. Certainly isn't what T'Kumva or Voq did. But now the Federation is losing, and losing so spectacularly that Saru at a first glance mistakes the loss for total, even though a status quo apparently is easily established in the end after all. Clearly something about the situation 15 months into the war is
drastically different form what Saru saw six or even seven months into it, even when we later learn it factually matters little.
Timo Saloniemi