I returned seriously to the game a few days ago with two of my seven characters at lvl50+/- and in BfA with several unfinished quests. In hindsight, I either didn’t have “Chilling Message” or had abandoned it in one of my prior entries into the game. Whatever the case, I leveled my warlock to lvl58 in BfA, and decided I’d buy the Dragonflight expansion, which I’ve yet to do. I was able to resurrect the “Chiling Message” quest, and entered Shadowlands with trivial quests ahead. What to do? Do I muddle through Shadowlands til the Campaigns are finished? Do I stay only until I’m lvl60? Do I go back to BfA for the last 1-1/2 levels to 60? In other words, do I get to go to Dragon Isles at lvl60 regardless of how I got there, and will I be missing much by not being in Shadowlands at all?
As soon as you hit level 60, regardless of how you got there, you should get the quest to start dragonflight (if you have the expansion purchased). If it doesn’t pop immediately, you may have to go to stormwind or relog to get it to pop up.
Whether you want to or not is completely up to you. But with DF being the newest content, that’s where most players currently are. BFA and SL content isn’t going anywhere, so you can always return to it if you want to see the story at some point. Or you can experience it on alts as well.
How you play the game and where you go from here is something only you can decide. 
I’d suggest creating a new Dracthyr and running it through their starter area before making the decision.
The Drac starting area is very well done and does a good job of introducing you to the various capabilities they have. It starts at level 58 and is finished by level 60. Can pretty much be done in an evening of play.
IMHO, Shadow lands was one of the worst expansions. They really didn’t start making it somewhat player friendly until quite late in the expansion and there’s still a lot of holdover stuff from it’s bad days.
Thanks, guys!!! I continued with BfA to lvl60 (about an hour of play), and got the invite to DF. BTW, I did enter SL, and immediately disliked it. I’ll fool around with Drac, although I had difficulty creating a character I could relate to. And hitting with my tail seems a bit of a reach — LOL. I have to research a bit more on Adventure Mode after I get the campaign done on my main.
Just remember you will still need to do some of the side quests and/or professions on your way to 70. You can’t hit 70 on just the campaign missions.