What game has the most "realistic" and controllable mechanics for melee combat with a focus on swordfighting?

examples could be:
Skyrim
Mount and Blade

Blade Symphony
Chivalry: Medieval Warfare

What games would you recommend that are available on GOG?

Mount and Blade.

I don't know any game that has really good melee combat. I suppose it'd take some innovation to design a good system and then teach players to use it. I suspect mainstream gamers would never learn it, so it'd be a rather niche feature.

I guess Mount & Blade kinda tries to do it, but I also think it falls way short. The system is quite clumsy and imho not that well controllable or satisfying.

The katana in Shadow Warrior 2013 can flow relatively well and be quite satisfying, but forget realism, you'll be using superpowers. It's way better than the average, but still doesn't have that much depth to it. In the end, they wanted to make something that works even for the basic player who expects click-click-click to result in whack-whack-whack and that's it. If you pay attention, you can control it much more than that, but it doesn't work that well every time.

EDIT: looks like someone did a let's play of sw2013 focusing on katana & shurikens only: https://www.youtube.com/watch?v=B6PxLXrabEk&list=PLxE07zulM4tvMwvfLVbMydOixznEetgCT
(plus a couple less common organic weapons)

I haven't played it, but I heard Die By the Sword is challenging and uniquely rewarding in it's sword handling.

Seeing as "realistic" is in quotation marks, definitely
Jedi Outcast and its sequel Jedi Academy

The focus isn't only on light saber combat though since it takes a while to get your own light saber. In Jedi Outcast the 1st third or so of the game is a surprisingly good FPS.

In scale 1 to 10:
1. Die By The Sword:
- realism - 4. You can do some weird movies. If you add orcs and necromancers, you should know that melee combat and world itself are way too far from being realistic.
- controllable - 8. You can control only one arm, but to very high degree.
2. Superhot:
- realism - 1. You instakill everyone (with katana), even if you silce their legs. Humans do not die when losing legs. In case of losing legs they die because of bleeding. UNREAL and DISPLEASING.
- controllable - 5. Only few movies, but it is a ok-drawback if you can control the time itself.
3. Mount and Blade (With Fire & Sword in my case):
- realism - 8. It seems to be reallistic.
- controllable - 8. You can freely change from saber to whelllock pistol and beat the sh!et out of swedes, moscals, cossacs, tatars or poles and lithuanians.

Every above game can be brought here.

Not sure Amazon still sells games that aren't keys for clients, but I have Dark Messiah on there and it is DRM free. It's a great melee combat game too, I agree. I think it sucks for stealth though.

Blade of Darkness. Has to be the ultimate melee combat experience, hands down. It WAS available on GOG.

While there weren't really any swords in the game (or am I wrong and there were?), Dead Island had one of the most gripping melee combat setups I've had the chance to play - though this was solo.

Not a game in itself but a mod for Skyrim by DukePatrick:

https://www.nexusmods.com/skyrim/mods/78303

I first played his hand-to-hand combat mods in Oblivion. Seems he got rid of them but has moved on Skyrim. His mods incorporated momentum as a major component of combat. It was wonderful!

For me it's Jedi Academy, without question.

The melee combat was so good that I played regularly from around 2003 to 2011 when the community finally dwindled away. It's one of the very few online games that I really got into.

I'd say For Honor as far as man on man melee combat goes. It feels like real fighting- it's reactionary and focuses on countering what your opponent tries to do, shifting the grip on your weapon and the direction of attacks to get an edge. But it falls apart when you have to face multiple opponents and the single player campaign is limited but fun.

Otherwise the stamina and inertia based system of the Souls games. Hit someone with a heavy 2 handed sword and they stagger, time a deflection and you gain a massive riposte opportunity. Dance around using a fast light sword against a heavy opponent is awesome fun. Shields work like they should. I know some people think the stamina system is unrealistic, but watch a boxing round and see how exhausted the fighters are after only a few minutes- and that's without them even carry a weapon, think how exhausting it would be to be swinging a warhammer.

I don't like button mashers and combo based systems, even though they are fun in the right games- the OP was asking about realistic.

Curse of Monkey Island.

Six years ago, I would probably have said "Clang".
But of course - that never came to fruition.
https://www.theverge.com/2014/9/19/6531001/neal-stephenson-swordfighting-game-is-officially-dead

https://www.kickstarter.com/projects/260688528/clang

Edit:
If I ignore this restriction: I would say "Mordhau".
https://store.steampowered.com/app/629760/MORDHAU/

https://www.polygon.com/2019/5/9/18539881/mordhau-steam-melee-combat-physics-review

And maybe (maybe) add "For Honor":
https://store.steampowered.com/app/304390/FOR_HONOR/

https://www.polygon.com/for-honor-guide/2017/2/15/14611430/battle-controls-combat-fighting