This item is underspecified
Here are two things that will happen once a DM introduces this item into their game.
DM: "The evil wizard utters a word of power, and his crystal orb glows with a sickly green light! The light engulfs you and you feel yourself growing weak. What do you do?
Barbarian: "I smash the orb with my axe."
What happens when someone hits the orb? What's its AC? How many hit points? Does anything happen when it gets destroyed?
DM: "You meet a gnarled old woman on the side of the road. She's selling apples. There's a blue ring on her finger, and two crows sitting on her shoulders. One of the crows is watching you suspiciously. What do you do?
Wizard: "I spend two minutes haggling with her over the price of her apples. During that time, I use weird insight on her twenty times. On average she fails ten of them. What are her ten most interesting secrets?"
What happens when you use weird insight on someone? Do they notice and get angry? If they succeed, are they immune to subsequent attempts? If they fail multiple times, do you get a new secret each time? Do you get their "most interesting" secret, or can the DM just tell you what they had for breakfast?
If you don't answer these questions, the DM will have to make something up the first time the item is used. (And we can't tell you a magic item rarity if so much depends on what the DM makes up.)
Assuming reasonable rulings, Rare is probably fine
The Driftglobe is uncommon. The Amulet of Proof against Detection and Location is uncommon.
Casting 1/day sickening radiance, a fourth-level spell, is good, but it's not better than the Rare wand of fireballs or wand of binding. This orb is better than a normal sickening radiance cast because you can move it onto your enemies over and over -- but it's worse than a normal sickening radiance cast because your enemies will just destroy it. (I'm guessing the Orb has AC16 and 20hp, and it doesn't do anything too surprising when destroyed.)
If the weird insight really lets you learn someone's ten most important secrets after two minutes of talking to them, then it's way too good and should be considered an artifact. Instead, I'm assuming that this power:
- lets you learn someone's single most important secret if they fail their first save
- succeeding on the save means they're immune to the effect for a week
- if they fail more than once, you just get the same secret over again
- people always notice the telepathic invasion of their mind and become hostile
which makes the ability roughly as good as charm person or detect thoughts.