can the technology in cars, especially new ones, cause sleep problems

There are lots of electromagnetic exposures in the car that could affect sleep.  The lighting and display screens and blue light are one.  Microwave (radiofrequency) radiation from the Bluetooth, WiFi, etc built-in to the car is another.  You should measure with an RF Meter to see what the car is producing.

Another exposure can be lane assist/blind-spot assist (radar).  Then you have the ignition system and arcing (high frequencies) and alternator, and all of the metal moving parts in the engine compartment.  Lastly that I can think of for now would be steel-belted tires.

Cars are LOADED with unnatural EMF to summarize.  It could most certainly interfere with sleep among many other issues.