Thanks for your great question. There are actually a variety of answers depending on the type of job you get as a chemical engineer and the type of employer.
If you end up working for a large company, such as a large chemical or other industry product manufacturing company, you could end up working on a team with engineers, scientists, technicians and others. Depending on the company's products, you may work with different types of engineers- chemical, mechanical, electrical, etc. It's likely you would work with chemical engineers and chemists and biochemists. But depending on the type of job you have, you could also interact with people from multiple departments with backgrounds in business/financial management, marketing, law (eg, intellectual property), information technology, training/workforce development, international/policy affairs, etc. Some may not have any science/engineering background. If you prefer and depending on the job and specific project you are working on, you could also work more closely with chemical engineers and chemists. There is a lot of flexibility.
On the other hand, if you work in a very small company, you may work with fewer chemical engineers/people with similar backgrounds and would be working more with an interdisciplinary team. Since there could be a very small number of employees, you could be one of the few chemical engineers. You could work more closely with your direct boss in a smaller company.
In summary, there is a lot of flexibility and it depends on the type of job and the employer- both the type of employer (eg type of company) and the size of the company).