Cher responds to Kate Bush breaking her Official Chart record with Running Up That Hill, topping Believe

Splitting hairs......smh

Not sure I agree that it is splitting hairs when we're using the achievement as some measure of longevity.

Not really. This record wouldn't count if Kate had been unfortunate enough to die before this success. The same way that Elvis' 2005 reissue #1s don't count (he would have been 70, breaking Louis Armstrong's record of 66). We're only counting this record because Kate has survived. She has had no active part in the promotion or recording at her current age.

Cher, in contrast was alive, currently recording, and actively promoting a new, front-line recording and release, who still holds the record for such activity. Both Kate and Elvis gain the accolades of a current release, while having recorded and promoted it several decades earlier. The latter having died in the meantime.

This isn't a re-issue. That's why she has a record for longest time taken to reach #1. Kate reworked the song in 2012 for the Olympics, and that version reached top 10. This song, however, is the original recording released in 1985. Effectively making her the oldest female to score a #1.

It's not the original physical record selling (12KB1 and KB1), it's GBCNR850002. Downloads and streams weren't available for the original release, so it's a re-issue for the digital era. Original recording (as indicated by the '85' in the cat no. above) yes, but not original issue/release. It's not even on the same label as original (EMI), it's now on Fish People.

The Olympics version if it's a different song and recording should have a separate entry. Such releases always did when CIN/Guinness compiled the chart.

Anything pre-2007 released physically and then becoming a hit as a digitial release since 2007 are in the same situation: The digital editions are effectively re-issues. Although there are a couple of examples whose physical release was so close to the digital release, it makes their chart runs a bit less clear cut:
3 Lions (2006 reissue) and Fairytale Of New York (2005 Reissue), whose physical editions were still selling in the digital era. Just 2 examples off the top of my head. There are probably more,

This Kate Bush example (and many others, including Christmas releases), are far enough apart for them to have a physical deletion and new digital edition distinct enough to have their own chart entries. Although, different rules apply if we are counting 'recordings' rather than 'releases'.

Like I say, I'm pretty sure this record would not count if she had died (as Elvis did). Yet it does count because she is alive, even though she has done the same amount of work for the digital release as Elvis did for his 2005 reissues. She claims the record by a quirk of physical survival rather than recording or promotion.

Well that applies even more to Vera Lynn if you look at it that way

Indeed it does, although that was for the album chart. It was also a very clear new release in it's own right, of old material in the same way that any Greatest Hits is. Kate's is neither new release (even the download/streaming edition is over a decade old, let alone the original vinyl-only release), nor new material.