Is it polite to use "delinquent" for a colleague at work?

You are misinterpreting the usage.

According to Dictionary.com, the definition of delinquent is:

1. failing in or neglectful of a duty or obligation; guilty of a misdeed or offense.
2. (of an account, tax, debt, etc.) past due; overdue.

Or from Merriam-Webster:

2: being overdue in payment

Your colleague is not calling you a troublemaker or law breaker. They are saying that the item you were supposed to file is late (definition 2). When used to mean past due or late, the word is not offensive or rude.

It is very common to say something like "Your time sheet is delinquent, please submit it immediately." Or if you don't pay a credit card or loan payment on time, then that payment is considered delinquent. It is quite common in professional settings and your colleague is not insulting you.

It sounds like you're delinquent in "action" is being used as opposed to you are "a" delinquent in personal character, which changes the entire context of the sentence. The use of the word "a" alters the impact delinquent carries.