It's important to note that Byleth does need to be careful offstage, too. Their tether recovery is able to beaten out by a long-lasting hitbox put in the path of the tether if the Byleth player doesn't mix-up their timing, meaning that Byleth will want to mix-up when they recover, just like every other character. However, tether recoveries are unable to be two-framed, meaning we only have to worry about avoiding edgeguards and ledgetraps.
When Byleth is on the ledge, they have some mixups to help them escape. Some of the more common ones include: Jump > Side-B (good for hitting someone far away or on a plat), Drop > DJ > Side-b (regrabs ledge, hits the ground in front of the ledge), Drop > FF> Up-b (grabs the side of the stage, and jumps off it, putting us above ledge and slightly offstage), Drop > Up-b (can hit opponents standing right by the ledge, or jumping right by ledge, and sets up for follow-ups). Make sure to only use these as mix-ups, as if they are constantly used they are very punishable.