Exactly that

Your single biggest problem is wildshape - no magic items are designed to function for a Druid in wildshape. Some, like rings, and necklaces can potentially function if the are left on the animal. However they don’t resize so a ring on your finger is likely to fall off if you change into something like a spider or cat. That or it’s showing up on the creature making it obvious that it’s a Druid in wildshape not a normal animal. There were a number of items in 3&4e that were made for Druids but they would have to be homebrewed. If you are looking for items that are useful and thematic outside of wildshape here are some possibilities:
COMMON ITEMS:
clothes of mending - some DMs have the clothes show the damage from under wildshape, these fix that.
Beads of nourishment and refreshment - talk to the DM maybe you can create these along with healing potions
UNCOMMON:
Bag of Tricks - having a bunch of critters you can pull out when needed is right up a Druid’s alley
Boots of Elvenkind - always appropriate for a Druid
Broom of Flying - lets you get closer to your stars - and no attunement needed.
Cap of water breathing - Druids need access to all environments
Elemental Gems (any/all) - if it’s elementals it’s good for Druids
Gloves of Swimming and Climbing -having extra movement rates seems appropriate for a druid
Goggles of the Night -allowing you to see at night seems appropriate for a for a star druid
 Javelin of Lightning 
Nature’s Mantle
Ring of Swimming Staff of the Python limited to Druids and a couple of other classes
Wand of Magic Missiles - the missiles can be shooting stars
RARE:
Bead of Force - the DM could have these be star shaped
Bell Branch - Druid or warlock only item
Bowl Commanding Water Elementals - anything dealing with elementals seems Druid/nature related 
Brazier Commanding Fire Elementals - like the bowl above
Censor Controlling Air Elementals - like the Bowl above
elixer of Health - your still a healer so …
Handy Haversack - everyone wants these
Mace of Disruption -clerics have Turn Undead, Druids should have this.
Ring of Animal Influence
Ring of Free Action
Staff of healing - lets you use other spells while still doing reasonable healing
Staff of Swarming Insects - another Druid limited staff
Staff of the Adder - another Druid limited staff
staff of the Woodlands - a Druid only Staff
Staff of Withering - another Druid limited staff
Stone controlling Earth Elementals - like the other elemental control items
VERY RARE:
carpet of flying - like the broom but even better
Horseshoes of the Zephyr - anything that leaves no tracks seems appropriate for a druid
Ring of Shooting Stars - right up a star Druid’s alley
Robe of Stars - another star themed item
Scimitar of Speed - one of the very few ways a Druid can get 2 attacks in a round
Staff of Thunder and lightning

these all seem to have some connection with  or specific usefulness withDruids or with star Druids in particular, there are still lots of highly useful general purpose items good for any class but you can search for them on your own.

Keep in mind some of these items have changed in 2024. The broom of flying for example now requires attunement

Most rare or very rare items require attunement  that wasn’t part of the OP.

Also a Star Druid will basically never be using their Wild Shape. As that is the source of their Star Forms.
Honestly any good item for Druid in General is gonna be good for Star Druid. Things that boost your Defenses, Give you Free Casts of Spells, or Augment your Spellcasting DCs/Attacks Rolls are basically gonna be your go to.

One of the Star Druid's specialties is zapping enemies with Guiding Bolt, so anything that raises your spell attack modifier is going to be helpful, like a Moon Sickle.

I recently created a homebrew magic ring for the Star Druid in my game. It is thematic and useful. I often like to customize magic items to have an additional ability like this as it makes interesting and special for them.

The Ring of Whispering Stars

• Description: This elegant ring is crafted from polished obsidian, inlaid with swirling patterns of silver that seem to subtly shift and shimmer like distant galaxies. A single, multifaceted clear crystal is set as the centerpiece, within which tiny, starlike inclusions appear to twinkle. When you wear it, you sometimes hear the faintest, almost imperceptible whispers.
  
  
• Properties:
• Arcane Empowerment: While wearing this ring, you gain a +1 bonus to your Druid spell attack rolls, the saving throw DC of your druid spells, and the damage dealt by your druid spells.
  
  
• Foretell the Stars: Once per round, as a reaction when a creature you can see within 30 feet makes an attack roll or saving throw, you can glimpse the celestial patterns and grant that creature advantage or disadvantage on the roll. You can use this property twice per long rest, and expended uses are regained after a long rest.

Requirements: Druid class, attunement required