yellowspanner
Exegesis of that Guardian article follows, as I can quite see that your opinion of the newspaper may preclude close reading:
Not all countries do things the same way.
In France, a woman retains her birth name in the eyes of official administrative bodies throughout her life, whether or not she takes her husband or successive husbands' surname(s) on marriage. Take Jeanne, who was born Jeanne Dupont and then married Philippe Moreau. For census, etc., purposes, her name is Jeanne Dupont épouse Moreau.
The married name is added, often in a separate column on official papers, but the birth name is used first on passports, ID cards, etc. It's not a question of people being guilty of "changing their name but not changing their passport" - if you ask for your French passport to be changed to include your married name, it will be added in second place, after your birth name.
If you create software that only reads the first surname, as is the case here, it won't read her married name.
If a French woman moved to the UK, chose not to apply for a UK passport but to carry on using and renewing her French one (something that was entirely legal while the UK was in the EU and that many people probably did because French passports are far cheaper than UK ones) and then applied for settled status, she will have submitted her French passport as requested, in good faith.
The fact that the UK's settled status applications system is not set up to deal with this type of fairly basic issue regarding married women's surnames shows that it is - call me all the names you wish - not fit for purpose.
Refusing to extend the deadline when some EU member states have done just that in acknowledgement of the difficulties UK citizens abroad may face preparing their application is an interesting example of the type of bureaucratic rigidity some are inclined to accuse the EU of showing towards the UK. With a hint of something else thrown in.