So sad to lose you, yet happy for whomever has the pleasure of working with you next.
Regarding the interpretation that the entire clause following preposition "for" is the object of the preposition "for":
"For" needs a noun object, which can be either a word or a noun clause. But "who(m)ever" is a relative pronoun, so the clause in which it occurs is not a noun clause unless written in the rather awkward form "I am happy for someone's having the pleasure, etc...," where "having" is a gerund, i.e. a verbal noun. To have a more fully idiomatic noun clause following verb "am happy," drop the preposition and insert "that," as in "I am happy THAT someone has the pleasure ...." It's a different construction from the original "...happy for whoever has ...," and expresses a different meaning.
"whoever" / "whomever" is a compound relative pronoun, which combines into one word both an implied generic antecedent meaning "anyone" (referenced as "-ever") and the simple relative pronoun ("who," "whom"), to mean "anyone who," "anyone whom."
In " ... happy for whoever has the pleasure ...," "whoever" is correct because the relative pronoun is the subject of verb "has;" but that does not make the entire clause the object of "for." The object of "for" is the implied generic antecedent "anyone," expressed as "-ever" in the compound relative pronoun "whoever." This is awkward for syntactic analysis, but absence of explicit antecedent, as object of preposition "for," does not require, much less justify distorting the syntactic character of the entire following clause.