Magento, as an eCommerce platform, will allow you to add/edit/delete items, attributes, and categories. You can also create advanced product types, such as grouped products, or bundled products (kits). While you'd need to spend some time familiarizing yourself with the options and deciding which features you'd like to use, I don't believe that curating items will be a big challenge for you with Magento.
Magento Open Source, the more popular version of Magento, does not include a Gift Registry, but you can add one with an existing Magento Extension, such as: https://marketplace.magento.com/magenest-module-gift-registry.html
If the registry is at the heart of your business, you may want to invest into a more custom extension if you want to fine-tune this experience.
Subscriptions are another feature set that will require an extension. This will partly depend on the payment gateway that you'll be using. You can see examples at: https://marketplace.magento.com/catalogsearch/result/?q=subscription#q=subscription&idx=m2_cloud_pro...
There are also Membership extensions that would help with automatically switching a customer's user group based on a subscription. User groups can potentially be used to give shoppers access to particular products or features (with some customization) or special pricing (by default).
Subscriptions would require a user to register for an account, but in general, Magento also allows for guest purchases where the shopper does not need to create an account. Guests still receive order confirmations by e-mail.
Magento does support user accounts, which you can manage as a website administrator. Customers have access to their order history, address book, and other useful features.
There are many e-mail marketing and multichannel marketing platforms that connect with Magento. These range from Mailchimp and Klaviyo through DotDigital, Emarsys, Listrak, and Bronto.
There are extensions to integrate Xero accounting. Keep in mind that some of these will require a service fee, as they're SaaS companies that help to manage these connections for you: https://marketplace.magento.com/catalogsearch/result/?q=subscription#q=xero&idx=m2_cloud_prod_defaul...
You can use Magento to manage your inventory. This includes allowing Magento to show products as "Out of Stock" when the inventory dwindles down to a predetermined quantity. If you have a POS, WMS, ERP, OMS, or other system managing inventory for you, you can connect it via Magento's APIs. If you're using a popular system, there may even be existing connectors that you can leverage.
Magento can handle localization in terms of currency and language, but there are facets to this, so it's best to plan out your more specific goals and use case.
You can get data from Magento to other systems via API. You can run reports from Magento. You can also export some data via flat file (ex. CSV) natively, such as product data. There are extensions that you can add to Magento to add even more flat file data export capabilities.
Magento's native themes have been mobile responsive for many years now. Additionally, the latest versions of Magento 2 allow you to leverage Progressive Web Apps (PWA) for an even more mobile-friendly experience.
With Magento, you're going to want to optimize for speed. This involved working with a good Magento host and following development best-practices.
Magento is, generally speaking, SEO friendly. You may want to add a blog or take other steps to enhance your SEO, but it adheres to generally accepted best practices.
Magento will allow you to set up different storefronts (with unique domains) for different stores that you're operating. I'm not sure that you'd need this for the "Stores", which may simply be categories, however, this may come in handy for setting up versions of the store in different languages/currencies.
The "Wishing Well" concept seems to be more unique. I'm not as familiar, so I'm not sure exactly what you'll need.
These notes are predicated on you listing and selling the items, regardless of how you fulfill the orders, which could include having other vendors drop ship for you. You'd be curating and managing the product catalog. Allowing shoppers to add "any" product to their wishlist, even if it's something that your site doesn't offer, would be more complicated.
All in all, it's a pretty unique use-case. Magento would give you A LOT of the building blocks to start from, but in my opinion, you'd still need to be prepared to work on some of the more unique and custom features that you're seeking. What you're looking for is not necessarily available "off the shelf" with Magento, or any eCommerce platform that I'm familiar with.
Best of luck!
