Are there any engineering/programming jobs that use Arduino?

Engineering is a study that applies to any field. Answering your specific question, I am not 100% sure about the Arduino BUT, you can apply your skills and knowledge on any embedded programming and any robotics job (Amazon, Microsoft and military).

So, your options are quite big, you just need to identify what do you like and which role alignes more to your career goals.

The short answer is simply, "yes". I can tell you from personal experience, I was once heading a project that involved a remote-controlled test link, and we didn't have the equipment available immediately. As a work-around, I used Arduino as the control unit. We ended up using other equipment vendors, but for prototyping, it worked fine. I don't think I'd hesitate to do the same again if it was convenient, and I'm sure other engineers have done the same. As for programming languages and programming in general, realize that there are very few areas today where computers are not used, and I don't know of any engineers who don't have at least some familiarity with one or more programming languages or at least operating systems. At the very least, an engineer would have a computer, and that computer would most likely be running Windows, MacOS or one of the Unix-like systems. Also realize that many applications, notably the Microsoft tools, have their own scripting languages or mechanisms, which is just another language. In general, it would be tougher to avoid exposure to computer languages than to use one.

Please investigate Udacity...they offer relevant online Nanodegrees (6-12 month commitment) using software of today-now. Don’t lock yourself into one like Arduino.

Hi Melvin! Arduino is a great tool that lets you easily get your foot in the door in interfacing hardware and software. By all means keep experimenting with them if you already are. Check out Processing, which is just one of many toolsets you can use to integrate your hardware Arduino creation with a complimentary computer program.

With that in mind, I would say that it's pretty rare Arduinos are used in production mechanical engineering systems. Most common industrial control systems are purpose built to be reliable in a variety of conditions: extreme environments (manufacturing facilities can be hot or cold, dusty, etc.), high duty cycle (they can be powered on for years), integration with existing control systems, and more.

I'll cover two areas of exploration I'd recommend you look further into. One is a common control system called Programmable Logic Controllers, or PLCs. These are purpose built to do things such as control motors, servos, read inputs and outputs, temperatures, and more. Often times PLC manufacturers will have a flow or graphical based design system (usually a computer program) for configuring PLC actions, so there may be little to no programming in the sense you may be expecting depending on the exact use case. You can get started with some real PLCs for under $100. Check out vendors like Automation Direct. Here is a YouTube overview on PLCs that looks like it may be a good introduction.

The second recommendation I'd make, and much more programming heavy, is to look generically at what are called RTOS - Realtime Operating Systems. These are small computer operating systems designed specifically for controlling critical systems. A common example would be something like the engine management system in your car. RTOS can handle critical functions that occur hundreds or thousands of times per second such as throttle readings, sensor data, and more. FreeRTOS is one example of an open source RTOS option, which is a great project now sponsored by Amazon. There are a number of development boards similar to the Arduino you can get for under $20 that can run these systems. A great options is the STMicro development boards. There is an added benefit in that the STM microcontrollers are quite prolific. The ESP32 boards are also a great choice, as they contain WiFi, bluetooth, and more (though less widely used in industrial settings). Check out this AWS FreeRTOS getting started guide.

I hope those options give you some insight and next steps.

I am absolutely sure that they are out there.. We once used a Raspberry Pi and an ODroid C2 board for a project we were working on. The beauty of technical jobs is that they are only limited by your imagination. Learn as much as you can, be curious and you will find that you can use any technology to resolve most issues you will come up against!