Following on from your posting in October 2019, I believe you are based in the UK and that any sales of your prints would be from the UK. Therefore I don't think you can rely on the Bridgeman decision as that occurred in the USA (the Southern District of New York to be precise).
We haven't had a recent test case in the UK which clearly sets out the legal position here with regard to this situation. The Government's Intellectual Property Office has provided guidance (see page 3 of this pdf
) in which they say that as a general rule slavish photographic copying of out-of-copyright works will not be sufficiently original to qualify for new copyright in the digital image. (Incidentally the photographs in the Bridgeman case involved images on film, which arguably required greater skill on the part of the photographer).
There has been considerable academic debate on this subject about the number of choices a photographer would make in order to faithfully reproduce of a painting, and whether these would meet the 'originality' threshold. The current test, set out by the Court of Justice of the European Union, which the UK courts are required to adopt, is that originality only occurs where the author or artist (ie photographer in this instance) has reflected his or her individual personality in the creative choices which led to the work being made. I think it is fair to say that the current consensus is that, given the limitations on the photographer when faithfully photographing a painting, there is little or no scope for any personal creativity. The choices are limited to a choice of lighting, exposure and colour correction. While these choices may require skill and experience on the part of the photographer, it is also true to say that with modern digital photography, many of the choices can be automatically handled by the camera and/or post-production software. The degree of latitude available to the photographer in such circumstances is very limited indeed.
In other words, I can't give you a definitive answer either way, sorry. However for what it is worth, I can't find a copyright notice, either embedded in the image itself or on the Christie's website, and so it is possible that they are not actually claiming that copyright exists in the digital image. The second thing in your favour is that museums, galleries and the like are incredibly reluctant to see a case like this go to court for fear that a decision will go against them and thus open the flood gates to widespread legal copying which will seriously damage their sales of reproduction prints. For example in the case of the National Portrait Gallery v Wikimedia Foundation
the NPG decided to settle, with the gallery allowing medium resolution digital images to be freely copied from their website, while retaining the ability to sell or licence high resolution versions which are not put online, rather than take the matter to court. Perhaps Christies will take the same view.