Can confirm this one works for GOG.

https://github.com/zero334/Dawn-of-War-Widescreen-Fix/releases/tag/1.1

Was hoping GOG would have worked some magic and included some build in widescreen like they did with second sight but this is the best we have so far.

This is for the main game+winterassault,
Dark Crusade and Soulstorm have support for higher resolutions by default.

Is it nice proper widescreen or screen will be stretched or with black bars on sides?

nope, all stretched. need fov-correction.

Unfortunately it is stretched, I prefer it over black bars on sides but it is what it is.

I Also recommend this camera FOV mod, makes the game more enjoyable
Its compatible with ALL games

https://community.pcgamingwiki.com/files/file/33-warhammer-40k-camera-zoom-mod/

Back in the days for me only one lua file be enough to make Camera Zoom mod worked.

There is widescreen in patches for DoWWA. With same issue as in newer initially support widescreen issue with camera fov.
Also minimap broken.

Mini map broken in such mods too for DOWWA.

Im sure i did play some version (retail on some patch, latest, steam on some patch before or after sega+steampipe maybe current version) and i get more proper widescreen. I cant say how it is now in current steam version and how in gog (lazy to check steam lazy to find a way to buy gog version from russia). As i get it, usual game widescreen mechanic is just resolution with interactive (mouse movable on that sides) black bars. During gameplay too. Im sure i saw version with black bars in main menu but wide gameplay parts including broken minimap issue.
I faced broken minimap issue and im never install widescreen mods (only camera zoom). So there is version without black bars, right?

Technically there is widescreen resolutions in all 3 game. Native 16:10 support for DC and SS and native 4:3 for WA with 16:10 resolutions added in patces in game (not available in ConfigOptions.exe).
No buildin or mod way fix minimap. Minimap is core RTS element. Im agreed for widescreen fix mod buildin only if there is no issues limitations with it. If someone did find a way to fix minimap.
If there is still no proper widescreen mod - it SHOULDNT be pre-installed. GOG are repackers, but official. Mods supposed to be optional. You can install mod to offline drmfree games you bought, but you cant uninstall preinstalled ones.

So sometimes resolution not mean screen size and aspect (and not mean quality). Like Framesrate not always related to Refreshrate.

FYI: I use that mod on the non-GOG version (installed by CD, "Gold Edition") and it looks like this in 1080p:
https://ibb.co/9bPDCzn

For me thats fine

Yeah, thats how it looks for GOG as well, 1080p but the UI is stretched, I am fine with it as well.

How non modded GOG (offline) work? Did it render black bars? If did - on 16:9 or 16:10? Did mini map broken on buildin widescreen and did it broken by mods?

As seen on screen - it did broke mini map for mod (btw maybe downscale a bit help it (a bit same), eg 1600x900 on fullhd+ displays?).
There is not only visible distortion, but map no more interactive if it is looks like that (in my old experience). Thats another important role of minimap. And on screen above it is tinies map. On large one UI did make it less visible.

Camera Zoom mod anyway is a highly recommended. Especially for non-16:10 cause game actually render upper/down sides outside of the screen. Ingame that solved by increased zoom. In Config benchmark are not so important (cut head of spacemarine). This happen on all 3 games on all versions on all resolutions (except 16.10 for now good old 16.10 widescreen displays).
There is minot issue from mod - maximized out will make landmarks blured/mist. Easily solved by just a bit zoom out of default (back to normal default) :)

This also can be "fixed" by console command to remove FOG. General ENB Series library with default preset also remove FOG (with minor else visual changes) without console.

Offtop. TO make console available and working in all modes - "wh40dow.exe" -forcehighpoly -console -dev. Cheats also working in all missions in all games (reveal FOW at least).
Any arguments from hoster in Lan require same/none arguments for other player to connect. In case of pre-steam versions.