Shared inventory removes the sync problem and replaces it with an allocation problem.
Shopify shares one inventory pool across channels, so the failure mode is not divergence but competition for the same unit.
Which locations may fulfil online orders is a business decision with real consequences for shop floor staff.
Safety buffers stop the floor selling out from under itself, and almost every multi-location retailer needs them.
Bundles, gifts and buy-X-get-Y consume stock in patterns your forecast does not describe.
They are not synced so much as shared — retail and online draw on the same inventory records, so a sale in the shop decrements the same stock your website sells from.
The full guide has the formats, the deadlines and the worked examples.