Yoshi's Story, Battlefield, and Small Battlefield are all top tier stages for Byleth. Final Destination is the worst stage for Byleth. Everything else is matchup based and personal preference. Your bans and selections will vary based on how you play and what your opponent is like.
Battlefield (BF)
This stage has the highest ceiling and the same horizontal blast zones as Final Destination and Small Battlefield. This stage is a triplat stage, which is extremely beneficial for Byleth. Up Special sharks the top platform and enables 50/50s even if Byleth started a sequence from the body of the stage. The side platforms have normal extensions and this stage also allows for laddering, if Byleth chooses to go for them. At ledge, nair can kill confirm (no rage) as early as 50 or 60 percent raw. The platform layout also aids in ledgetrapping, juggling, and catching landings. This stage is one of Byleth's best and is a reliable pick.
Small Battlefield (SBF)
This stage has all the benefits of PS2 but it lacks the drawback (size). This stage has the same body and blast zones of FD, but it has platforms. This makes it automatically better than FD, if it is legal. This stage is fantastic and almost always a good pick. Byleth can corner carry from any part of the stage. For Byleth, these platforms make it FD 2.0 (but better) and this stage has platform extensions, total tech traps, and up special 50/50s like normal. Byleth can deal almost 80% with one hit confirm combo (and this is quite funny).
Final Destination (FD)
No platforms, no walls, the blast zones aren't special, it's not a good pick for them. Byleth doesn't really get anything out of this stage, but loses a lot of options. Can make approaching more difficult
Yoshi's Story (YS)
This is another triplat (good for Byleth) that has walls and downward slants at ledge and has thinner blast zones than FD. The blast zone floor is also much higher and the ceiling is the same. The top platform auto spaces up special for the grounded throw from the floor of the stage. The platforms still give us more combos and tech traps like mentioned before. Byleth kills very early on this stage and has many-many recovery mix-ups with the tether due to the wall. This stage is great and is comparable to BF.
Lylat Cruise (LC)
This stage is often complained about, but Byleth does a fine job on this stage. The platforms can be extended on, but Byleth will have to account for slants for autocancel timings and pressure. Since they don't exactly have much use or opportunity for jablocks, the slants don't interfere with their tech-chasing much. Tech-chasing up the slants can make FN1 cover more character's knockdown. The slants permit down tilt to hit more character's ledge hang, even if it's only a handful more of them. Up special is extremely limited to nab wall jumps on this stage. The only spots Byleth can use to wall jump are the tiny walls that consist of the ledge and the walls on the very underside of the stage and are far out of the way. This stage has blast zone distances from ledge similar to Town and City. The slant can also impact certain confirms and can make them more consistent or require a different execution than normal. This execution different also occurs on other stages and is not a con, as you react to the victim to link to the finisher. Vertically, the blast zone ceiling it lower than it is on TC/SV. This makes it easier to KO vertically, barring confirming off the high side plats on Town. Byleth can KO as early as 53 (not an forward smash) on this stage and can do normal hit confirms and neutral plays. The tether has no issue recovering on this stage and Byleth can recover from basically anywhere so long as your area have a direct line of sight to the ledge. This stage is a solid pick, and should be considered for keeping.
Pokémon Stadium 2 (PS2)
This stage's platform layout and blast zone distance from ledge is notably beneficial for Byleth. However, the stage is wider than Final Destination. This is a bit obnoxious but it's not always a big deal. The ceiling on PS2 is the same as on FD, but this stage has platforms. There are also walls under the center of the stage that you can use to wall jump off of if you need a stall or a recovery angle mix-up. This stage is good, solid, and is a fine starter.
Smashville (SV)
This stage has the exact same blast zones of TC, but the stage body itself is significantly smaller. The center platform is also static and in a similar spot relative to TC's center platform. This stage HEAVILY rewards stage control, which is a trait that Byleth excels in. The platform permits us to cover landings and pressure the platform well, and there isn't a lot of space to run away from Byleth to. However, the ceiling is as high as ever and the side blast zones are farther away from the ledge than Town. This isn't really a big deal, considering that by those %s Byleth would KO on town, Byleth can just edgeguard for free. This stage lets Byleth hold a fundamental-based snowball and permits their strong platform extensions at most any position of the stage. This stage is a solid pick, and should be considered for keeping.
Town and City (TC)
This is where things get interesting. The stage is FD with close side blast zones and platforms. Even if the stage is FD (but better due to close side blast zones) the platforms give Byleth pressure and extensions that FD simply just doesn't have. Byleth also can get KOs at really low percentages off ledgetrapping. Vertical KOing is worse, but Byleth mainly confirms to KO horizontally. The ceiling is a tiny bit lower than BF's, the low side plats and center plat combo and tech-chase well, especially with IDJ involved, and the high side plats grant an up special grounded throw auto-spacing. This opens more combo and kill options. The center plat can be laddered with and the combo tree available to Byleth can go up, down, offstage, center stage, or wherever they want. On the other hand, their opponents will also have these benefits and in matchups like Roy/Chrom, Byleth absolutely will not go here as it will benefit them significantly more than it will benefit Byleth. This is just better FD. Consider it, but it might be banworthy.
Kalos Pokémon League (Kalos)
This stage is FD with walls and plats that Byleth can incorporate into their ledgetrapping. However, it's still FD with big blast zones which means they will generally kill later, but also die later. This is kinda MU/player dependent but it's not really a good stage for Byleth. It just functions. It does give more than FD though! Consider it, but probably a ban.