Ortho Grid in QGIS straight and curved

I’m really new to GIS tools.

I’m trying to make ortho projection maps of all the countries. I’ve downloaded Natural Earth Data and QGIS. I imported the data files by dragging them into QGIS. I added a Grid to my default projection by using the "Vector->Research Tools->Create Grid…" menu option. Then I densified the grid with "Vector->Geometry Tools->Dentify By Count". Then I switched the Projection to a custom projection defined as the Proj String:

"+proj=ortho +lat_0=23.868 +lon_0=121.0521 +x_0=0 +y_0=0 +a=6371000 +b=6371000 +units=m +no_defs"

It almost looks exactly how I’d want, but the grid lines are both curved (like I want) and straight across the globe.

I’ve tried poking around the menus and searching the internet for what I did wrong, but I haven’t had any luck yet.