This is hardly a niche use case
Yes it a niche no single silver bullet exists here for managing time itself.
The specific workflow each business needs to manage that information is wildly different with “multiple sources for their products” being a force multiplier then with even more complication in how each business needs to present that data to customers , lists, checkboxes, multichannel,etc. And then join ALL OF THAT with shipping estimates or other business rules. That is Niche.
It’s a process that has to be tailor made for each online business on shopify from existing platform features.
Product Titles/Content, Variant Options, Transfers(next_incoming_date), Metafield Definitions, Line item properties , Collections , Other(product images,skus,barcodes). Or as @JoesIdeas outlined Metafields or Tags.
Product Titles or Content
For a single variant product the fastest way is to put the lead time in the product title, don’t change the SEO handle. For themes that hide invalid variant option combinations with multiple variants having less than 2 options put the lead time into a new variant-option itself so the variants title contains the dates. Remembering the 100 variant limit.
For multichannel presentation of lead time Titles or Content(Descriptions,Images,Vendor) is the only way, and it is the most persistent method that automatically works in themes, notifications, channels, etc.
Transfers - next_incoming_date
If using the transfers system use variant.next_incoming_date https://shopify.dev/api/liquid/objects/variant#variant-next_incoming_date
Which can be adding minutes for single-variant products using a custom-liquid block in OS2.0 themes:
{{ variant.next_incoming_date }}
Products with multiple-variants will need javascript customized as well in most themes. Or just show all variants incoming dates in a table/list with a forloop.
Metafield Definitions(mfdfs)
Native metafield definitions(mfdfs) is the new hotness for stuff like this for online sales channel stores.
Where once created and selected in OS2.0 themes they can be added in moments to product templates.
Though metafields apps like @JoesIdeas recommends, or spreadsheet apps, can provide conveniences for specific workflows.
https://help.shopify.com/en/manual/metafields/metafield-definitions/
https://help.shopify.com/en/manual/metafields/displaying-metafields-on-your-online-store
(note that if you create a mfdf to hold a list you cannot edit items in the list later in admin /shrug)
Line Item properties
To have it during checkout per item/variant use line item properties on those products in tandem with the method use to store that data.
Theme and Notification templates may need to be customized to display that info as needed.
https://community.shopify.com/c/shopify-design/product-pages-get-customization-information-for-products/td-p/616503
Collections
Manual Collections can be good for categorical lead times, i.e. 1 week or 1 month etc, to help customers shop by expedience or patience.
Templates in theme and Notification may need to be customized to display the correct collection info.