You can use

J’ai oublié à qui elle veut parler.

As you said, in this context (complément du verbe), you use “qui” when the pronoun replaces someone (usually a person) and you need “à” because in French it is “parler à quelqu’un”. So the rule is “préposition + qui” for a person ([…]avec qui tu manges, […]de qui tu parles, […]pour qui tu travailles, […]chez qui tu vas…).

Note that the “ce à quoi” and “à quoi” are both possible in this context , but “ce à qui” is wrong.

Je me demande (ce) à quoi tu penses. (what)

ce is however necessary for a direct complement (See here for more details)

Je fais ce que je dois.

Step by step :

• I forgot = J’ai oublié
• who = qui*
• she wants to talk = elle veut parler
• to = à*

You need to fill the blank in your translation with the (*) missing part.

I forgot who she wants to talk to.

J’ai oublié ____ elle veut parler.

→ J’ai oublié à qui elle veut parler.