Do a consumable iOS product REQUIRE restore functionality? I am developing a game, and I want to submit it to the AppStore, but I don't know if this will be a cause for rejection:

Say a player can buy 100x arrows for 0.99$. Do I have to provide the user the ability to restore the unused arrows in order to not be rejected by the AppStore?

I really don't want to use a server to store the number of arrows the player has, as that would be off the budget.
No.

In the requirements and guidelines for App Store Review (shown below) it does not say anything about a return mechanism. It does however say "you should make sure you have a restore mechanism for any restorable in-app purchases." What this means is explained here.

App Store In App Purchases guidelines:


  3.1.1 In-App Purchase:
  
  
  If you want to unlock features or functionality within your app, (by way of example: subscriptions, in-game currencies, game levels, access
  to premium content, or unlocking a full version), you must use in-app
  purchase. Apps may not use their own mechanisms to unlock content or
  functionality, such as license keys, augmented reality markers, QR
  codes, etc. Apps and their metadata may not include buttons, external
  links, or other calls to action that direct customers to purchasing
  mechanisms other than in-app purchase.
  Apps may use in-app purchase currencies to enable customers to “tip” digital content providers in the app.
  Any credits or in-game currencies purchased via in-app purchase may not expire, and you should make sure you have a restore mechanism
  for any restorable in-app purchases.
  Remember to assign the correct purchasability type or your app will be rejected.
  Apps should not directly or indirectly enable gifting of in-app purchase content, features, or consumable items to others.
  Apps distributed via the Mac App Store may host plug-ins or extensions that are enabled with mechanisms other than the App Store.
  Apps offering “loot boxes” or other mechanisms that provide randomized
  virtual items for purchase must disclose the odds of receiving each
  type of item to customers prior to purchase.
  Non-subscription apps may offer a free time-based trial period before presenting a full unlock option by setting up a Non-Consumable
  IAP item at Price Tier 0 that follows the naming convention: “XX-day
  Trial.” Prior to the start of the trial, your app must clearly
  identify its duration, the content or services that will no longer be
  accessible when the trial ends, and any downstream charges the user
  would need to pay for full functionality. Learn more about managing
  content access and the duration of the trial period using Receipts and
  Device Check.
  


This line basically means


  if you delete the app, move to a new phone, whatever, your purchases
  will no longer be available on that device. Restore Purchases asks
  iTunes what of the available in-app purchases you've paid for.


It does say "should" which you could imply to mean that it is not forced but highly suggested.