Quads instead of Tris after split

Sometimes I like to mask some parts of a low poly object and split the masked area.

However it becomes a challenge if I need to make some changes (manipulating the edges/vertices) to the split object afterwards because the split parts become tris.

It would be nice if the edges & vertices were quads and aligned with the existing ones.

Have you tried applying a quad remesher?

And maybe this video will be helpful:

On something with such low poly count the quad remesher doesn’t keep your objects shape. I can see in your picture that you have a slight bend to [at least] one of your objects.