Byleth doesn't join any side. Similar to how it went in Fire Emblem Fates: Revelations. And then after the five year timeskip, they meet up with Claude in the Goddess Tower, and they explain what has happened. Dimitri and Rhea having teamed up to stop Edelgard. And since Byleth hasn't sided with any of them, they have slowly gone corrupt. Dimitri with his obsession on killing Edelgard, Edelgard and her lust to abolish the Crest and Noble System and not being able to control her rage; Rhea's obsession on seeing her Mother again and wanting to kill Byleth for "running away" with the Crest of the Flames.

So their first target is Edelgard to calm her down and not kill her. After infiltrating the Adrestrian Empire, they defeat her and while waiting for Byleth to kill her, Claude then intervenes and gives a speech on how "Teach never chose a side, they believe there is a much better route for us to achieve our goals without mindless bloodshed." Edelgard will probably breakdown and hug Byleth.

Alternatively, Claude and Edelgard could be waiting in the Goddess Tower, Claude greets them normally, whereas Edelgard runs up to Byleth and hugs him/her tightly, slowly breaking down into tears.

Next are their goals to stop Dimitri and Rhea, after meeting them in the Tailtean Plains and fighting them, Edelgard calls out Rhea by exposing her of the corruption she has down to the past, so Rhea could create the false religion and how the Historical Documents plastered the Church of Seiros as the righteous and good. After defeating and calming Dimitri down, Rhea either dies from her wounds or joins them (She could survive and leave the war) and confesses of what she had done, only wanting to see her Mother again.

After the battle against Dimitri and Rhea. Byleth, Edelgard, Claude and Dimitri focus their eyes on TWSITD to stop Thales and a newly revived Nemesis, while also having to kill Edelgard's Uncle and other members. Cinematic of all four attacking Thales and Nemesis, with both Edelgard and Byleth getting the finishing blow while Dimitri and Claude helped distract them. Afterwards, the Empire, Kingdom and Alliance finally live in peace, unified. With either the Church of Seiros being abolished or being used under another guise.