As I've already noted in the threads in the Canadian and Australian subforums...
No, we almost certainly will not see 2022 Charles III coins. Both for sentimental reasons - everyone's still mourning QEII - and for practical reasons.
The biggest hold-up is in getting the new royal portrait of Charles III approved. They do not have any stock portraits archived away that they can just whip out and use at a moment's notice. They couldn't prepare a portrait in advance, as it would have been against protocol, not to mention common decency, to start designing the Queen's successor's coins when she wasn't dead yet. And designing a new coinage portrait, frankly, isn't high up the list of priorities for a new king these days. I suspect it will be at least a month before they get around to choosing the artists and having a portrait sitting, and how long the process through to finished coins then takes would depend on how fussy Charles III is in choosing likenesses which he approves of. Queen Elizabeth II was notoriously easy to please and never rejected a portrait, but back in 1936, new king Edward VIII took so long to choose his portrait that he'd abdicated before they could use it on any coins.
So the new portrait of Charles III isn't going to be ready until late 2022, or early 2023 - which will be too late to strike any 2022-dated Charles III coins. If they do what they did in previous monarch transitions, they will continue to strike 2022-dated coins, featuring Elizabeth II, up until the new portrait is ready to go. If a country desperately needs circulating coins and the new portrait isn't ready by January 1 2023, they will most likely continue to issue 2022-dated coins with the old portrait.
As for the question of 2022 coins becoming valuable, well... for the most part, 1936 coins aren't valuable, and 1952 coins aren't valuable either. Mainly because lots and lots of people kept them, as "souvenirs of the old king". So it's much easier to get nice Unc examples of 1936 and 1952 coins, compared to, say 1933 and 1950 coins. And partly because, as I mentioned earlier, the mintage period for "2022" coins is likely to end up being over a year, so total mintages will likely be higher for 2022 than for surrounding years.
But if you want a hot tip on QEII coins that are likely to appreciate in value, I'd recommend the 70th anniversary of accession coins that everybody made earlier this year. Britain, Canada, Australia, New Zealand, and probably a bunch of other places all made coins for that occasion. Queen Elizabeth II made it to her 70th of accession, but didn't make it to her 70th of coronation (which would have been next year, since she was crowned in 1953).
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis