Will my app belong to the non-trader status if there are no in-app purchases and profits through the app?

Trader status is not linked to a specific app but to your organisation.

I extracted and outlined some key points from: https://developer.apple.com/help/app-store-connect/manage-compliance-information/manage-european-union-digital-services-act-trader-requirements/

To determine if you're a trader, you should consider a range of non-exhaustive and non-exclusive factors (see those listed on page 2 in the EC’s Guidance), which may include:

• Whether you make revenue as a result of your app, for example if your app includes in-app purchases, or if it's a paid or ad-sponsored app — especially if you're transacting in large volumes;
• Whether you engage in commercial practices towards consumers, including advertising, or promoting products or services;
• Whether you're registered for VAT purposes; and
• Whether you develop your app in connection with your trade, business, craft, or profession—meaning that you’re acting in a professional/business capacity. You're unlikely to be a trader for EU law purposes if you're acting “for purposes which are outside your trade, business, craft, or profession.” For example, if you're a hobbyist and you developed your app with no intention of commercializing it, you may not be considered a trader.

Regardless of whether you’re an individual developer or organization, if you have a legal status associated with a business activity, that would suggest you may be a trader.

IMHO, from what you wrote, you develop the app in connection with your business, hence you should be considered as a trader.

Does your organisation also make/sell the IoT device? What sort of organisation is it?

Here's a scenario where you may not be a trader: the IoT device is made by someone else, and your organisation is an open-source project that makes an unofficial app to control that product. If the open-source project is just a group of volunteers with no business structure, then you might qualify as not being a trader.

In just about every other situation, you are a trader.