Is selling design services provided by freelance designers at a price higher than the cost after reaching an agreement with the client, and selling these services to other companies at a price that includes a profit for both the seller and the other company, considered permissible or forbidden?

This is not a sale, but rather an ijarah (definition) (leasing/hiring) for work to be done, which is a liability. It is permissible for the ajir (hired person) to hire someone else to perform the work, unless the first hirer stipulated that the ajir must perform the work himself, or if the work is of a nature that varies with individuals and no one else can substitute for the ajir in performing it. Designing websites and logos does not vary with individuals; rather, the objective is to achieve the desired outcome. Therefore, there is no harm in the questioner subcontracting the work, whether he is a hirer or a hired person.