I just put in for a transfer to another location my company has there
and will transfer back to my original location when we move back. I
don't believe I should have to go and change my state of residency,
drivers license, car registration/plates, insurance etc) since I
consider where I am now my permanent home. It's just a temporary
relocation.
While this arguably works for the common law concept of domicile, as a practical matter, if you live someplace for the majority of a year, and often more than 30 days, you are considered to reside there. You should change your driver's license, car registration/plates, insurance, voter's registration, etc., unless there is an extremely compelling reason to do otherwise, and not just different tax rates and more bureaucratic inconvenience.
A planned three year stay doesn't cut it, especially, if you don't own a home or have a residential lease on a residence in the state you want to claim as your residence.
The main exceptions would be someone who is in an institutional setting, such as attending college residentially for nine months a year while supported by their parents, in a prison, or in military service, where different conventions sometimes apply.
Legally, could I leave everything as is since the apartment
"technically?" isn't mine (I'd just be staying there with her?
No. Residency and who owns or leases the place where you are living are two entirely different things. The many people who don't have a lease or own a home are still residents of the places where they live. For that matter, even if you are not a citizen of the U.S., you can still be a resident of a particular state or locality.
I'd be filing my taxes as someone that commutes out of state to work
and residing in their current home state etc.
Nope. For state income tax purposes, you reside in the state where you sleep a majority of the nights in a year. There are sometimes more complicated rules that apply to apportion income between states, but that is the strong general rule.
Is there anything I'm missing/not aware of that would make this a bad
idea?
Or is this a normal thing people do commonly and I'm overthinking it.
This is a bad idea and not a normal thing that people do commonly.
At a minimum, it will leave you with bureaucratic tangles and at risk of serious state tax audits (which, reading between the lines, seems like the most plausible reason you are thinking about this approach). At worst, you could be exposed to liability for having improper tax payments and car insurance in place, and potential criminal liability for misrepresenting your residence. It might not end up coming to a head and being a problem, but the probability that it will is significant.