I don't expect any of the postcards' photos/images were taken/created prior to the year 2010.
Here lies the problem with your collection: All of these works are made within about the last 2 decades, if we are generous. That means, it is night impossible that the copyright on the work lapsed: The Berne Convention demands that copyright shall protect for at least 25 years after the death of a photographer. Most countries grant more, but that is the absolute earliest a copyright for a photo might expire.
However, most countries fall into the category to go for something similar to the united-states: "Life of the author + 70 Years" for natural people and "Publication + 70 years" for companies. For anonymous works, many countries take "Publication + 95 years" as an interpretation.
This means: under US law, on 1.1.2023 you may re-publish postcards that were published up to 1953 with a company claiming copyright, where the author died before 1954, or anonymous works published in or before 1928.
UK Law, Postcards would fall under Photography and get the same 70 years after the author's death as in the US.
But... "extenuating circumstances"?
Copyright law doesn't have such. Copyright law has exceptions: Fair Use in the US and Fair Dealing in the UK.
Fair use is an affirmative defense. It means you say "YES I infringed your copyright but I do this for a reason that is allowed." It is a 4-prong test:
Purpose and character of the use, including whether the use is of a commercial nature or is for nonprofit educational purposes
Nature of the copyrighted work
Amount and substantiality of the portion used in relation to the copyrighted work as a whole
Effect of the use upon the potential market for or value of the copyrighted work
Just look at the factors... The copyrighted work is a postcard. If having a text on the back, it is a combined work of the photographer and the writer, it might be seen as a piece of art (which has better protection) or correspondence, so.... let's say it's neutral. 3 is the amount used, and here we need to republish at least one side completely, which generally is discouraged in interpretations. However, a collection of items is generally not market usurpation for selling postcards, and there might be a heavy transformative character in the character of the use, especially if each postcard becomes part of the collection and maybe even is commented on.
Commentary and Critique, which is part of prong 1, is commonly regarded as very strong for fair use, allowing to use up to the whole work. For example, the "H3H3 case", revolved around such.
Fair Dealing isn't defined in statute, but is generally a two-prong analysis:
does using the work affect the market for the original work? If a use of a work acts as a substitute for it, causing the owner to lose revenue, then it is not likely to be fair
is the amount of the work taken reasonable and appropriate? Was it necessary to use the amount that was taken? Usually only part of a work may be used
These mimic the Fair Use Factors in some regards, but not everywhere. A collection of photos of items is more likely not substitute for possession of the item itself, but it is hard to determine necessity without knowing more about the site's planned layout. In general, if you want to comment and critique the item, it's often seen as allowing larger amounts to be reproduced. The quality of the republication might also be a factor, especially in the substitution prong.