Welcome back!
So you have done at least some of The War Within as well?
At 75, there is no way to access Dungeon Finder for Dragonflight dungeons. Your sources were correct that you would ask Chromie to set you in Dragonflight timeline to access them, but as you have found, Chromie is done with you once you hit 70.
However, you should be just about in a position to solo Dragonflight dungeons now, so you can just walk in and fight your way through to complete the quests.
Your gear is maybe too wesk right now. At 75, you should be able to wear … ilevel 550 maybe? at least 520-530.
If you pop in to your friendly local Auction House, you may be able to grab some Greens and crafted Biues for a couple of hundred each.
https://undermine.exchange/#us-moon-guard/search/cat=4.1.5_20/lmin=500/lmax=580/rmin=2/rmax=3
Just make sure that the actual item you are buying is wearable by a level 75. Since they changed the AH, it has been too easy to pick the wrong item.
I don’t know how it would go for you at ilevel 460, but if you get your item level up to 520-ish, I’m sure you would have no problem, at least with Normals.
Or you can wait until you hit 80, and breeze through them once you have geared up a bit. It won’t take you long to hit 80 from 75 - a matter of hours, maybe one long play-session.
But at level 80 before you have geared up you will be very weak because of scaling, with your levelling gear, so at that point buy some stuff at the AH or get your initial gearing out of the way and get up toward 600 before you go into them, or they’ll take forever.
Raids are a different matter. You won’t solo Dragonflight raids without much more gear, and maybe not then, so you should probably check Group Finder / Manual / Legacy Raids for people farming DF raids. Or join a Guild or Community to find others to group with you.