I understand that you created a task, then on the contact record you are trying to edit the task to add this same task to a task queue but the option is greyed out. Please let me know if that's not the case.
I understand how frustrating this can be, not to be able to add a task queue from the contact or deal. Let's see that together to see what we can do.
I tried on my portal and from the contact record, on the activity tab, on the "tasks" tab, I was able to edit an already created task and assign it to a task queue and then save my changes.
1. Who created this task? It could be a permission issue? 2. Who the contact is assigned to? Is it yourself? You might not be able to edit such contact. 3. Are other users seeing the same behavior? 4. When you hover the greyed out option, is there a message? If yes, what does it say? 5. Have you tried with an incognito window to see if this helps?
The more info, screenshots (without sensitive/confidential information), and details you can provide, the better the Community can assist.