I've had lots of dreams about Pokémon ever since I got full-time into it! Some of them I won't tell here, but there are a few I can spill the beans about.
First thing first, I have recurring nightmares about glitches in my games, or glitched Pokémon. The earliest I recall was encountering a glitch Pokémon called Cirilia, which looked like Sky Forme Shaymin with Jirachi's star-shaped head. I have also dreamed about a glitched Diancie in my Y game, about my Black 2 cartridge going kablooie and displaying Pokémon names as random strings of text (e.g. "A wild Fjejfhewfs [Wailmer] appeared!") and a messed-up version of the Kabu battle in Sw/Sh. Needless to say, considering the amount of glitch dreams I have, I always get uneasy when my games start remotely malfunctioning.
I also have recurring dreams about Pokémon plushies, which are usually happier ones than the above. It's usuallly about me getting a Pokémon plush from a crane at an arcade in my city (that doesn't exist in reality, or barely resembles its real-life counterpart). However, after getting my Mimikyu plush buddy... I started having dreams about having two Mimikyu plush buddies - the one I already have, and a new one that comes out of nowhere. For the latter, I blame a funny series of fics in AO3 where a Trainer accidentally adopts a second Mimikyu after mistaking it for her first.
Lastly, I have had dreams about the human characters as well. Those are the ones I refuse to tell here because of their rather... intimate nature, especially involving some of my husbandos favourites. The most recent one (from earlier today!), however, was rather tame. It was just Ingo wandering into a shop in his PLA get-up... plus a pair of round glasses not very unlike his monocle in his special costume in Masters. I went "almighty Sinnoh, as if you couldn't get any more handsome!" on sight, and he was receptive but also flustered. It was so cute!