I've thought of doing hardware design attempts on this before. My rough mental notes:

Ink:

• Ink tech is mostly the heads (either piezo or thermal). There are some projects on the web where people repurpose these for other stuff, so it's doable, but you then have to rely on parts from 1st party printer makers.

Toner (aka "laser"):

• Toner and drums are cheap and made by many 3rd parties. Design around whatever models are easiest to get clones of, don't reinvent the wheel.
• Similar for coated fuser rollers (hot rolly bit that melts the toner to the paper).
• To put the image on the drum you will need either a high res LED bar (only available 1st party?) or a spinning prism + laser (probably easier to get parts for to make).
• Work around prism spinning stability issues by attaching a honking great rotational inertial mass to it.
• Stick to single colour (single laser, single drum, single toner) to begin with; colour is the same thing x4

Paper path:

• Modern printers folder the paper over several times in complicated ways. It's very space efficient.
• Stuff that: do everything flat and linear. The printer will be an awkward shape (long and thin) but will be many times easier to work, test and modify.

Electronics:

• Chuck a small SBC on it and keep the software as portable as possible to other platforms (not tied to the one micro/brand/peripheral set). This means using simple GPIO for paperpath sensors and standard buses like I2C for digital sensors. (My current work project has been burned by a microcontroller going out of stock, it would have been much better if we threw a more generic SBC at the problem).
• Best interface to throw high bandwidth sync'd laser pulse data (image) out of? For compatibility and headache reduction maybe a USB bridge chip to some simple SRAM that gets dumped as a row when the laser starts a row across the drum. Maybe that doesn't exist.

Extras:

• A printer that scans and prints with almost the same mechanism. Feed a page over the drum where the laser hits, record the reflected light intensity, produce a B&W (or maybe even grayscale) image from this.

Legal:

• Do it in a country where you are free to break patents for non-commercial use
• Commercial attempts: LOL I suspect the existing printer companies will own patents on everything including the concept of human vision. Be prepared to spend your entire life savings (and lifetime) in courts. They do NOT want more competitors.