Winquake has waterwarp. It is fast because the engine renders it to a strict 320x200 buffer in which the renderer stretches and applies a sine table to.
Also, waterwarp refers to the screen being warped. The term for the water itself turning is known as water turbulence.
The menu brown tint effect was removed because it relied on reading video memory which is excruciating slow in DirectX hence the black dither starting in 1.07 and after. Engoo is the only source port that properly recreates the effect, and is only fast in -dibonly. No GL engine recreates this, because doing it accurately would also require fragment shading as it dealt with intensity along a color ramp.
There is ONE accelerated source port that does recreate the waterwarp and the water turbulence faithfully via pixel shaders. It's DirectQ, and it's a bit lost (author intenitonally deleted the page for reitrement) so here's a binary. Requires D3D9 or 10 (most likely 10), and should actually be ProQuake server compatible. It also supports overbrights and fullbrights, and non-power-of-2 texturing.
Water warp was technically possible under GL back then, but it would be 'super slow' because it would have involved heavy use of glReadPixels (which not all vendors supported) and then manually modifying the texture it readpixel'd to, then applying the sin tables, and then reuploading the textures back to the (then really really slow) video cards that have poor upload and memory speed. Since texture size limits were small then, it would need many, many small textures to perform this on. It wasn't until 2001 that the PC finally got back at the Playstation and N64 in this area.
Darkplaces doesn't have GLquake's water turbulence because it would interfere and clip through walls and expose holes. It did used to have "geforce3 water" via early fragment shader (pre-GLSL), but it's been removed ages ago and wasn't all that faithful.
For what it's worth, id Tech 3 doesn't have water turbulence either.