Does my preparation of a projected budget for a client seeking an interest-based loan constitute participation in this loan?

Your work in the office is permissible unless it is accompanied by an unlawful act. Every budget you calculate is permissible unless you know that the requester will use it for an unlawful purpose, such as an interest-based loan. This is because it falls under aiding in sin and transgression, which is forbidden in His (Allah's) saying, "And do not cooperate in sin and aggression." Therefore, you are not allowed to prepare these budgets, and you must clarify the matter to the company owner and the requesting company.