There is no agreement between the negotiators as yet on the repatriation of "stranded" goods after 1 January; the default will depend on any tax agreements between each of the member-states and the UK, virtually all of which pre-date the Single Market Act, and many of which predate the Single European Act (which will cease to grant any rights or impose any obligations on the UK at the end of this year).
In general it is likely that moving goods of any sort -- including one's own personal property -- from a member-state to the UK will from 1 January incur formalities, with a risk of substantial financial liability to the UK's revenue & customs agency by the UK person importing the goods even if that person is conceptually "re-importing" property.
Amazon also will want relief from liability under the law of bailment in England & Wales, and other specific contractual and statutory liability to the UK persons using the systems discussed in the article. The most obvious way to do that is for Amazon ("the bailee") to return the goods to any vendor in England or Wales ("the bailor"). The most obvious time to do that is well before 1 January after which either Amazon is exposed direct liability for import formalities or indirect liability to the (England-and-Wales) bailor.
Another obvious approach is to convince the bailors to waive their rights, effectively writing off their interest in the goods that are in the EU in Amazon's control, possibly for some financial consideration. However, Amazon cannot be certain that it can sell on any such goods because there is as yet no agreement on e.g. Origin (and documentation via certificate of origin) requirements, nor on the continued validity of safety marks and other product labelling. Although it's unlikely that anyone seriously wants existing arrangements to suddenly halt at the end of this year, there remains a risk that a substantial number of UK-sourced goods in the EU prior to the end of December may simply become unsellable in the single market in January (I am less sure about goods (esp. "Mode 5") sourced in the non-EU SM member-states or states that are non-EU&non-SM members of the European Customs Union (EUCU), or the bilateral CU states, and unfortunately somewhat failed at avoiding the trap of calling it all "EU" in this comment, and the trap of thinking the legal positions are probably homogeneous, i.e., there won't be operative side-deals between UK and Turkey before the end of December).
One very open set of questions involves "Mode 5" goods, wherein services are bundled with physical items. That includes warranties and guarantees for repairs, upgrade support including the upgrading of software that controls the physical items' operations, subscriptions bundled in with electronic book readers or the like, access to App Stores and similar. So far the UK government in particular has been focused on goods, not on services, including "Mode 5" services.
Flipping things around, Single Market vendors with bailments in England (and Wales) may be unable to guarantee the continuation of "Mode 5" commitments on goods in E&W. In E&W the retailer would be liable for making good on those commitments or on making the retail customer whole (e.g. by issuing a refund or replacement). FBA does not provide clear legal immunity from retail liability in E&W, and it is easy to imagine litigation brought by e.g. the Consumers Association and other bodies under the super-complaints procedure in the (UK) Enterprise Act 2002 if FBA goods purchased after 1 January cannot have software upgrades or lose access to SM-based customer support. (They are likely safe from liability for such goods if sold before the end of this year.)
(The law is somewhat different, and in relevant ways, in Scotland and Northern Ireland, but going into that would take too many characters :-) )
ETA: the issue here is the law of frustration of contract -- the expiration of the transition period in the withdrawal agreement may create frustrations notwithstanding careful drafting of contracts, and one possible result of a frustrated FBA contract is that the goods in question become involuntary bailments with Amazon as the bailee. This is a concrete risk for goods managed under contract with entities outside the UK.
Single Market sellers with goods pre-positioned in the UK would by default have access to UK courts if needed to exercise (or clarify) their rights as involuntary bailors. Thus it is possibly in Amazon UK's interests to move SM-vendor goods from the UK to an Amazon EU facility in the Single Market or return it to the SM-based person who is the vendor, and to do so before the end of the year and with the consent of the SM vendors.