First off you need to master google. You will first find that only some lcds use a traditional parallel interface, spi, i2c and sometimes serial are often used. And that is only because there is a chip attached to the lcd panel to sorta make your life easier. You will find that you can sometimes find the display without the helper chip and buy microcontrollers from all the major vendors that have a lot of pins for driving displays directly. saving on parts and cost.
As far as how to the engineers software and hardware deal with this? It is like learning to drive to a new to you grocery store, you look at the documentation (map) plan your attack and then go do it, sometimes you get it on the first try sometimes it takes a few.
There are examples for most of the popular display driver chips for most of the popular microcontrollers or architectures or the ones for the AVR (Arduino is not a microcontroller) might port directly or with a little help (the libraries might before Arduino yes, the sandbox/environment) or the mbed (another sandbox/environment set of libraries) or 700 others on github or wherever google takes you, or you just look at the datasheet and sometimes it takes minutes to get the display up sometimes hours.
Same goes for the hardware engineers, they look at the other part of the datasheet, the pinouts the electrical specs, power requirements, reference design, etc and plan and or just start on the schematic for the product/board.
Its all part of the job, professionals just do their job, not everyone is cut out or interested for this level work, some folks are better at applications, phone apps, whatever, video codecs, video games, etc, and some folks use libraries for these kinds of devices, but cant necessarily get their hands more dirty than that (Arduino)(some can but choose to not re-invent a wheel), and some can and will and love to get their hands dirty. Some write the libraries for others, the examples or drivers, etc. Some of the above mentioned jobs require wading through API documentation to learn how to make a gui program on some new to them environment, some have to read a book or look at examples or both to learn how to make a device driver for something, or look at the changes from the prior version of the operating system so they can tweak their existing drivers they are responsible for and/or write new ones as needed. Its all part of the job and how you get that title of "professional".
Yes you are on the right path, now with i2c sometimes it is just easier to bit bang, or bit bang first, then get through that and later, if ever, if supported by the mcu peripherals, use the mcu specific i2c peripheral. the latter runs better, but has a higher development cost (unless there is a good library already that just works) and is not portable. Bit banging, particularly with i2c, makes it so you can port your code from one mcu or family to another in sometimes literally minutes and have the display up, where if you use the built in peripheral that could be a long afternoon or day or week. A scope is not required but if this is your first time...required...or some other way to "see" what is going on, which you could kinda get by with another microcontroller polling gpio pretty fast and then using that as a logic analyzer. but for i2c you really want a scope because this is an open collector pulled up bus, and you can see when each side releases and takes over the bus which you cant see with a logic analyzer, and that timing may be important. the other fact is assume the manuals are at least a little bit wrong. they are never perfect, you have to "hack" your way through sometimes for lack of a better term.
the examples for other microcontrollers are going to help you with what registers to program in what order (sometimes matters, sometimes doesnt) and some values to poke in to those registers, which may or may not make sense when you compare the examples to the documentation for the device. you still have to come up with the basic i2c protocol support in order to deliver those register writes and perhaps reads (often you can get by with write only to some of these displays).
st parts are pretty popular, displays are a dime a dozen on ebay the nokia 5110 ones, there are some 64x64 and other sized oled ones, with i2c, spi, etc interfaces, plus a myriad of others. A handful of really popular display drivers (chips on the back) once you try one or two displays with those move on to the next...