As a Brit, I've never noticed NASA spelt Nasa before, and I'm on the fence about Unesco, not because I recall seeing it title-caps, but because it doesn't look offensive to me.
That said, when I googled for the title-caps variants of both words, I saw the Guardian, Independent and Times all used it for Nasa, but only the Guardian and Times seem to use it for Unesco. There was also a page from the NYT that used Unesco, so a counter example from the US, but even the UK government pages refer to it in all caps, as do most other UK articles.
I certainly find it a weird generalisation that "UK English" (sic) prefers title-caps, as we tend to like our abbreviated names and pretty much always use all-caps when every letter comes from a separate word, and only title-caps when we use runs of letters from each different word - quango (quasi-NGO), Bakerloo (Baker St-Waterloo), Beeb (compared with BBC), Lib Dems, etc. We also have a few things that aren't consistent for government things - Defra (always used to be DEFRA, but they seem to have rebranded), MOD (always caps), Ofqual (=Office of Qualifications, always title case), Ofcom (=Office of Communications, now seems to officially be title case, but always used to be OFCOM), UCAS (University and Colleges Admission Scheme, always all-caps), etc.
Maybe the stylistic choice is based on how pronounceable it is as a word, but whatever I don't think there are any hard and fast rules!
U.S. newspapers have a tendency to convert abbreviations to title case, even when everyone else uses all-caps. For instance, I've only ever seen "Covid-19" written in newspapers: everyone else always used "COVID-19", "COVID", or just "covid", or "the coronavirus".
