La traducción al español de esta guía está disponible aquí. ¡Gracias rainbown513!
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=3500959774
There is a fairly popular guide already by Hamod9041 showing how to integrate OpenMW with Steam. I would like to emphasize that it is not a bad guide by any means, but in my opinion this way is much better, and requires no replacing of files in Steam's Morrowind directory. Feel free to show that guide some support for their fine work, and this one if you found mine helpful.

Also, the instructions below are for Windows only. I believe it is possible to do all of this on MacOS or Linux distributions, but you will definitely need to make alterations to at least part 4 "Set launch options" to suit your operating system.

There is a guide below by The Chiefu - チーフ which describes a method for Linux using a script.
https://gtm.steamproxy.vip/sharedfiles/filedetails/?id=2877763412

Pretty straightforward. Just install Morrowind through Steam as you would normally. Since we wont be editing any of the files in the game directory that Steam downloads, you can use it as your data directory when setting up the game's data with OpenMW later.

Go to the downloads page on OpenMW's website here[openmw.org] and use one of the links near the top to download OpenMW either from Github (after clicking the Github link, scroll to the bottom, past the changelog and look under "Assets") or from the official site's file repo.

Run the installer exe for the latest version, and install OpenMW in any location you choose. It does not have to be in your Morrowind directory, or even anywhere in Steam's directories.

If you are on Mac OSX, there is a .dmg file in either of those locations. I don't use Mac and haven't in many years, so you're on your own from there.

If you are on a Debian, Arch, Fedora, or Gentoo based Linux distribution (maybe some others too), you may be able to find the latest version of OpenMW in their respective package repositories, in which case you can install it using your distro's package manager.

i.e on Arch
sudo pacman -S openmw
or Debian
sudo apt-get install openmw
Obviously if you aren't using sudo, replace it with whatever privilege escalation tool you use, like doas.

Once you have installed OpenMW, you will need to set it up with Morrowind's data files, otherwise you will not be able to use it to play the game.

Unless you are an advanced user, most people will use the openmw-wizard.exe to help with this. The wizard may detect your Morrowind directory automatically, but if it does not you will be able to define one manually. Select the file Morrowind.esm in the Data Files folder when doing this.

At the end of the wizard you may be shown options to import settings from Morrowind.ini and to import your add-on and plugin selection. The first option will pull in-game (and other ini-only settings) from the Morrowind.ini file located in the data directory you specified in the wizard. The other option will import enabled/disabled selections for plugins i.e any mods you may have installed. If you're starting from a clean install of Morrowind, neither of these options are necessary.

On Mac OSX and Linux distributions, there should be an equivalent wizard for you to use, though I have not tested OpenMW on either.

Once you're done setting up Morrowind with OpenMW, you can test to make sure it works by running either openmw.exe to run the game directly, skipping the launcher, or by running openmw-launcher.exe to start the launcher first. Starting the launcher first may be wise if you need to change any options or enable any plugin files,

Reminder: As I said before, this section will require editing depending on your operating system if you're using anything besides Windows.

In order to make Steam run OpenMW when pressing Play, you can right click on Morrowind in your library and select Properties. In the general tab, type the following into the "Launch Options" text box

"path\to\openmw\directory\openmw.exe" %command%

Edit the "path\to\openmw\directory\openmw.exe" part to the location of the openmw.exe file you use to run the game. For example, mine is "F:\Program Files\OpenMW 0.47.0\openmw.exe", but this may differ from yours depending on where you chose to install OpenMW earlier. The quotation marks must remain.

If you would rather start the launcher first before running the game, replace openmw.exe with openmw-launcher.exe.

At this point you should be finished, and you can try it now by pressing Play on Morrowind in your Steam library. You can check that it is running OpenMW by looking for the version information in the bottom right corner when on the game's title screen.

If the game launches as you would expect, then huzzah, you are finished. Enjoy playing Morrowind on a much better engine :)

Updated February 16

"Operation completed successfully (0x0)"
The file path in your launch options ends with a folder and not with the .exe file. It must end with either openmw.exe or openmw-launcher.exe

"This won't load my saves!"
OpenMW uses its own save format (.omwsave) and will not load save files made with the normal Morrowind engine (.ess)
There is a tool included that can theoretically convert them, but it seems poorly documented and is only usable from a terminal.
Most likely you're better off doing this guide from a fresh install.

"Check out Luxtorpeda, its better because etc etc etc"
If you're on Linux, its probably a good option for you. I have no idea because I've never used it and probably will never use it. But you don't need to write a dozen comments telling me about it. I know already, I promise.

"Opening openmw.exe runs a weird command prompt window in the background"
This didn't happen when I originally wrote this guide and seems to be new behavior as of OpenMW 0.48.0 or so. I have no idea how to disable this.
It's harmless and just shows a bunch of debug info. You can just leave it in the background and ignore it, it'll close when the game closes.

If you made it this far, I'd like to say thank you for reading all this and following along. This is the first guide I cared enough to write on Steam and I hope it helped you. Feel free to rate or leave a comment. Personally I think it is too long, but I wanted to be at least somewhat thorough.

If you are on a non-Windows OS and you can't get this to work, please keep in mind that I have only tested and played OpenMW on Windows, and although I occasionally use Linux, my help there is expected to be limited.

That's all folks. Drink water and have a great day.