Minimal Effect: Armor and Weapons not required

You can make viable builds as a Druid (and as other classes), without requiring the use of manufactured weapons or armor.

AC Options

Barkskin can help give your AC a boost (up to 16, but it is concentration), which isn't terrible. You're not going to be a Tank, but your Tankiness as a Druid is more in the HP soaking with Wild Shapes than in AC. In comparison, studded leather with a max Dex of +5 would still only give you AC 17. IN addition, when you WIld Shape, you will not have the benefit of your armor and have only the AC from the Wild Shape beast. Any spells supplementing that would carry over, so it's actually a plus for a build like this!

You can also have Absorb Elements prepared to help mitigate some damage types.

As you reach higher spell levels, Stoneskin is another option to mitigate damage.

Finally, the Investiture spells from Xanathar's give further help in mitigating damage and increasing offensive capabilities.

There are also Feats that may be worth it (Magic Initiate) that would let you take a 1st level spell (Mage Armor!) for a non-concentration AC of 13+Dex.

Weapon Options

As you stated in your initial question, Primal Savagery is a great cantrip for you. There are other options as well:

Shillelegh is a great early cantrip if you feel that a quarterstaff(doubling as your focus) is reasonable.

There are a lot of other cantrip and spell options for Druid that let you attack without the need for a manufactured weapon.

Common Gear

Getting by without some necessary items (like a pack to carry things, food, water, etc.) may be slightly more difficult.

You can use Goodberry to bypass your food (and maybe water) needs. But standard adventuring gear may be an issue. You'll need a lightsource if you don't have darkvision (although Produce Flame can give you light in a pinch as a cantrip)

Components/Focus

The biggest thing you'll have to figure out is spellcasting focus and/or component pouch as well as how you carry other things (but it sounds like that's not an issue since you don't want things.) If you decide to forgo the focus or the pouch, you may be limiting yourself to verbal/somatic only spells. If so, be careful in choosing your prepared spells for those with only V,S - but work with your DM and think about how/if you'd like to carry a focus or pouch.

Supplementing with Magic Items

There are a LOT of magic items that could help supplement a build like this. Ranging from the Ring/Cloak of Protection to wands/staves for Druids. My list above was really about how to make a build like this without resorting to items, but those are definitely options for you to review in the DMG if your DM is willing to make them available to you.

Going Commando

Going without arms and armor really is not a problem. You may have some limitations you wouldn't, but they wouldn't be immense. Play your flavor, you can do it well and not feel like you are creating too many difficulties that will stop you from enjoying your character.

This is almost balanced and ready for playtesting

In balance terms I think you have got this about as balanced as you can without playtesting, except for the 10th level feature. Fixing that then playtesting should be your next step. I expect you will find that some features are overpowered but the lack of slot recovery and the few underpowered feature balance it out overall. As usual I will still go through each feature and give some feedback.

Level 2

Bonus cantrip is good, you are giving access to something druids don't normally get so that makes up for that lack of choice compared to the Circle of the Land. I'm not fussed about the theme of Life/Death from Chaos but that is clearly what you are going for so that's alright. I would grant a more damaging cantrip like firebolt or acid splash to better suit the offensive theme.

1/20 chance of a free Wild Shape is cool and on theme. Though without the forms of Circle of the Moon and no casting in Wild Shape it isn't super useful. This feature is likely slightly underpowered compared to Natural Recovery but not too bad.

Circle Spells

• Crown of Madness: Yes! Totally on theme, a perfect choice
• Shatter: A good AoE attack spell that suits the theme. Good choice.
• Bestow Curse: Pretty good debuff spells that suits the theme. Not bad.
• Vampiric Touch: This is a little more death than Chaos to me. But I get that you want the healing from death type thing. Not a terrible spell choice.
• Death Ward: Not sure about the chaos part of this spell. It feels more like preventing chaos than causing it.
• Greater Invisibility: Not a bad option, it doesn't not suit the theme. Though you do have a lot of concentration spells to compete with it.
• Dawn: Was good before, still good now.
• Destructive Wave: Destructive chaos, basically built of this class. Good choice.

Most of your spell choices are pretty good. Some alternate suggestion for 7th level are: banishment, Evard's black tentacles, confusion, phantasmal killer and vitriolic sphere.

Also the suggestion by Rorp to give chaos bolt is awesome from a theme point of view. Unfortunately it is level 1 and doesn't suit the circle spell progression. I would consider finding a way to fit it in. Maybe instead of the free cantrip at 2nd level you give a 1/rest casting of Chaos Bolt.

Level 6

This is more balanced recharging only on a long rest. I'm not sold on the theme of it but it isn't an issue.

Level 10

Compared to the Circle of the Land this feature is way better. They get immunity to poison and disease, and charm and frightened from fey or elemental. Circle of the Moon get Elemental Wild Shape, Circle of the Shepherd get healing aura for summoned creatures, Circle of Dreams get a limited use teleport. You give advantage on all spell saves, all the time, with no restrictions.

As you say Yuan-ti Pureblood get this as a racial trait from 1st level. While this is support that the feature is not unbalance in general, it is still much stronger than anything the other circles get at this level.

The cantrip as a reaction thing is fine. It might be a little strong if you take my earlier suggestion to give a high damage cantrip but still not a huge deal. Combined with the other benefit is definitely pushes this into overpowered though. I would add some restriction to the magic resistance and cut this part for playtesting.

Level 14

Casting two spells in a turn 1/6 of the time could be really strong. However you will burn spells very quickly. I would limit it to not work on cantrips as that would just make it free damage with no cost. If this proves too strong during playtesting you could consider limiting this action to one weapon attack, Dash, Disengage, Hide, or Use an Object; the same as the action granted by the haste spell.

I love the theme of this ability and think you should stick with it, but be prepared to modify it if it proves too strong.

Why I think spell recovery is important

You say you want this class to be a primary caster druid. Every other primary offensive caster (Circle of the Land druid, wizard, sorcerer, warlock) have a way of regaining some spells on a short rest (sorcerer via sorcery points). Bard and cleric regain other magic-like abilities (Bardic Inspiration and Channel Divinity receptively) on a short rest. Circle of the Moon druids get their main offense (Wild Shape) back on short rests.

Most of these classes also have better offensive cantrips than the druid and don't rely so heavily on spell slots for damage. You are relying on spell slots and not giving a way to recover them. This puts you at a significant disadvantage compared to every other primary caster. That is why I have suggested it multiple times.