Lets get the easy stuff out of the way first. Fried is probably going to contend for the Cy Young again, so he is a lock. Spencer Strider may actually have the most upside in the rotation and could turn into an absolute star, so he is obviously in. Charlie Morton's best days are behind him, but the Braves have invested significantly in him and he should be more than a serviceable middle of the rotation starter even at his age, so he isn't going anywhere.
You may notice that I put an asterisk by Kyle Wright's name and there is a reason for that. I don't think he will start the season on the injured list and will be likely be on the roster, but I don't think he will have enough time to be ready to start that first week. I'll take the Braves at their word that he hasn't had any setbacks from getting a cortisone shot in his shoulder, but the clock is ticking and he still hasn't pitched in any spring training games. That means they may have to hedge a bit with their roster construction and they do have some options available to them if he isn't ready (this will inform my bullpen projections below).
Finally, we have the open competition for the fifth spot in the rotation and I give the slight edge to Ian right now, but my confidence in that pick is low. Bryce Elder has his warts, but I could see the Braves going that route if Ian struggles and Elder pitches well the last couple weeks of camp. Jared Shuster and Dylan Dodd should get some consideration as well as both have looked good in camp, but I'm giving the edge to Ian for now. I wish I could project Michael Soroka here, but he has yet to play in a spring game as he recovers from a hamstring injury, so we will have to wait to see him again.
Okay, this is going to take some explaining, so lets start with the easy stuff. Raisel Iglesias and AJ Minter are mortal locks as they are the anchors of the bullpen. Joe Jimenez was brought in to bolster the late innings, so he is in. Kirby Yates doesn't look quite like the guy he once was, but he has looked pretty good and the Braves owe him real money, so put him in there. Lucas Luetge gives the Braves another lefty even if the stuff doesn't jump off the page and he is out of minor league options, so he is in. Collin McHugh was a staple in the Braves bullpen last year and while he hasn't appeared in a spring training game as of this writing, unless we find out about an injury, he is a lock.
Of the Braves' offseason acquisitions, Nick Anderson may be the most interesting with his track record of success and his ability to miss bats. I'm going to wager that the Braves like what they see enough to keep him around even though they could use another lefty like Dylan Lee (more on that in a second). Anderson does have two minor league options, so that is a consideration here, but I think he ends up making the Opening Day bullpen.
That brings us to the obvious outlier pick here. Putting Dylan Dodd in the bullpen is a bit of a misnomer and a hedge at the same time. Above I was very skeptical that Wright would be ready to start the season just based on the information we have. Given that, having Dodd on the roster gives the Braves the option of spot starting him the first week of the season. Dodd also gives the Braves a lefty option that can pitch multiple innings out of the bullpen which could be very useful early in the season as the rest of the starters may not be quite ready to throw a ton of pitches to start the season. This is a very speculative pick, but Dodd has looked really good this spring and his versatility as a spot starter/long man makes a lot of sense here.
All of that said, I full expect Dylan Lee to be in the Braves' plans in 2023, but he has minor league options so rotating him into the bullpen after the Braves' early season needs change seems very possible. As for Jesse Chavez, I want to project him for the Opening Day roster badly, but he has not looked good this spring. I really like the idea that Mark Bowman floated in his roster projections of putting Chavez on a set throwing schedule in Gwinnett for the first half to keep him as fresh as they can and then revisit him in the second half if needed.