I think it's absolute bollocks.
If he'd said that King Charles had been impatient, curt, or frustrated, it would have been believable. I don't think King Charles is a man who suffers fools gladly, and at a time of such enormous stress it wouldn't be hard to believe that he might have been a bit abrupt.
But giddy and elated like a lottery winner?! Give over.
As PP have said, Charles Spencer hasn't been shy about speaking out over the years, there's no way he hung onto this for 30 years.
When Diana died, she had a very distant relationship with her brother. In contrast, she was on good terms with King Charles - apparently they used to pop in for tea with each other regularly.
I'm old enough to remember Diana's death. Charles looked genuinely distraught. He went over to accompany her body home, a courtesy that she wasn't automatically entitled to as she was no longer royal. And if the rumours are true, Charles was the one who argued with the Queen to ensure that Diana was given a full royal send-off rather than being treated like the private citizen she then was.
There's nothing at all to suggest what Charles Spencer has claimed is remotely true. And even if it were true, what disgusting things to make public, knowing the added scrutiny it will pile onto his nephews who he swore to protect.
He's a shitebag.
Oh - and you asked for links earlier OP - here's a couple but feel free to google as there are plenty more out there. Should you want to find them, of course...
https://www.hellomagazine.com/royalty/924147/inside-charles-spencers-complicated-relationship-with-sister-princess-diana/
https://www.sheknows.com/entertainment/articles/2803382/king-charles-princess-dianas-relationship-before-death/