Are there applications that create dynamic charts with dropdown lists as diagrams to show the overall process/procedures of an IT department as a part of the IT infrastructure, application portfolios, customer service, and operations?

I'm not aware of any perfect solution.

BPMS and ITSM systems can accomplish this but are cumbersome. Frankly sometimes a little less automation is a good thing unless automation comes entirely for free and doesn't require project work or training.

For this reason Visio is the most common one across three organisations. It has some dynamic and automation capability but it's ugly as sin and requires training. Something like lucid charts can be an alternative.

I've seen a lot of vendor solutions at Symposium expo, recent cloud startups that claim to solve the need, but I've been skeptical and don't have experience with them but Gartner covers the market and it's research arm can advise on the state of the market.

BPMN tools like Signavio can be helpful

Yes, options include:
Power BI + Visio for business (connectivity and ease of use),
Grafana/Tableau for IT monitoring (real-time insights),
Custom React + D3.js for web UIs (full interactivity and customization).

There are many more, and choosing the right solution highly depends on your specific use-case, budget and requirements.