Take a look at the trigger on the 1895.

This is a mechanism which will fail in the trenches of Flanders.
Hell, it makes the rest of the lever action look positively fool proof.
Now, this Mannlicher which you think is comparable, it has a receiver which, when cycled, opens on top & to the rear, just like any other bolt action. The only difference is it's not a turnbolt.
The 1895 has a receiver which opens on
two sides, above and below, and to the rear when cycled.
Not when the weapon is cycling.
that the thousands of Ross Rifles that the Canadians used.
Yes, and any Western army equipped with the 1895 in the same conditions that the Canadians faced will most likely have the same problems with the Winchester.
Eastern Front Mud different from Western Front Mud?
Regarding which weapons? The 1895 or the simpler Mannlicher? Find us some historical research that shows that the Russians actually thought the 1895 was a first rate weapon, as opposed to an emergency stopgap rifle purchased because they couldn't manufacture enough Mosin Nagants, and then you might have a point.
And as I listed, the Turks used their Winchesters in their Trenches in 1878 successfully
I've read that story as well, but it's almost irrelevant to the subject of the Winchester 1895 (and it's not exactly rock solid historial fact that the Winchester was the master of the battlefield in the Russo-Turkish War. It's mostly anecdotal. Wiki talks about modern artillery being deployed alongside these rifles.)
Because if you're comparing the merits of pistol calibre, short lever action Yellow Boy blackpowder repeaters (rimfire!) compared to trapdoor blackpowder rifles, you're not making an argument for the 1895 being a suitable weapon for the 20th century.