Is what I did considered Islamically forbidden: bringing a job to the office, then agreeing with the client on a percentage of the profits, then performing the work with an external team and keeping the remainder?

As long as you work in this office and wish to complete the work there, and obtain its seal, and your employer has assigned you to nominate some of your friends to work with them on the project outside the office, then you are a trustworthy agent for this work. An agent is obliged to do what is best for his principal and is not permitted to take any share of the profit without his principal's knowledge.