COH3 uses the EXACT same engine COH1 USED.
This is correct.
When Relic was under THQ, THQ pushed for Company of Heroes to be the most technologically advanced engine ever. First game to use DirectX 10, SLI/Crossfire support, Best Audio etc
Relic came out with COH Online afterwards which was good but ended abruptly due to Brian Wood's passing. He was in charge of the project and all things COH related.
Relic went on to make Dawn of War 2 which was basically the first mod of Company of Heroes 1 while they figured out what they were going to do with COH without Brian Wood leading the team.
Right after that THQ went out of business forcing Relic to produce COH2 without a publisher. They did not have the funding needed to make a brand new engine and did what they did with Dawn of War 2, just mod COH 1.
Due to Eastern Front mod gaining popularity, Relic decided to shut down modding for COH2 after the first Alpha once people figured out that the game was a mod of COH 1 (Shock Troops for example had the COH1 Tooltips for Rangers in COH1) They did like 10 minutes of work to create snowstorms without actually optimizing it and released it as is and called it COH2.
COH2 was launched in an abysmal state. Literally hot flaming dog trash. Then they shut down COH 1 multiplayer servers to force the COH1 player base onto COH2 which is literally the only reason why people bought the game. They had no choice if they wanted to play anything COH related.
Took them at least 2 years before COH 2 was even a playable game which is right about the time OKW/USF were added to the game.
Relic continued their failure with Dawn of War 3, releasing a train mess of a game and ignoring all early feedback for the game.
Age of Empires 4 came out of nowhere and like Dawn of War 3 had very little player feedback about what they wanted with the game which is why AOE4 has less active players now than AOE2.
So throughout this entire time all of these games used the COH 1 engine. Now with COH 3 launching they are going to continue using the COH 1 engine. COH 3 is using 1 CPU core. They plan on using 3 additional cores for texture streaming (Due to the COH 1 engine reaching its limits with memory they have to do a bandaid essentially for the new textures to work)
The game is still fundamentally a 1 CORE game which is a huge failure on Relic's part when you have an Indie company make a game that can use up to 32 CPU cores and 64 gigs of RAM (Ashes of the Singularity).
So far COH 3 does not have mappable hotkeys (a challenge for Relic since its something that they can't mod from COH1 and requires someone with actual programming knowledge)
Literally zero upgrades to the game engine. I am sure COH 3 will have a decent campaign but outside of that you are literally paying for the same product from 2006. Except instead of a DLC (which is what COH3 should be) you are being charged a full price game.