Is it correct to use "branch" to describe type of industry?

The best word for this idea depends on the context.

Within a company: As you allude to in your question, branch is appropriate for referring to other offices within the same company. To distinguish colleagues by role rather than location, you can use department or division. Many companies will have additional local jargon along those lines, like job function, organization, role, or silo.

Generally: For people who don't (necessarily) work for the same company, you can talk about different fields, industries, sectors, or specialties, depending on the nature of the difference. For example, industry and sector generally refer to very broad categories like finance, government, manufacturing, military, and non-profit, whereas field and specialty usually refer to different roles within the academic, engineering, and scientific sectors.

In American English, the term "branch" is used used in the corporate environment to describe the department of a company. You can have the Finance branch or the Development branch. I've also heard it used to localize project teams - the East Americas branch or the Bangalore branch. The metaphor that comes to mind are the branches of the corporate tree.

In the context of your sentence, I would suggest using the word "field" to describe an area of expertise. This term isn't limited to a corporate environment and can be used universally to describe groups of people - the programming field, the finance field, the sales field, etc.