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I am new to use QGIS (version:3.28.11-Firenze) and I have a question about the shapefiles and their projection.

I want to draw a map of Qing China and the World. So I first import Qing China's shapefile. The layer CRS is EPSG:2333.

enter image description here

And I then import a world map of that time. It shows no CRS.

enter image description here

Then, I found those two shapefiles are separated, and the world map is very tiny and far away from the China.

enter image description here

And I first tried to assign the CRS as EPSG:2333 to the World Map, nothing changed.

Then changed to EPSG:4326., but it looks wrong (but get much closer): enter image description here

After that, I tried to reproject (from the toolbox) the World Map from EPSG:4326 to EPSG:2333. But the position of the World Map doesn't change. (The Pink one is reprojected World Map)

enter image description here

Can you let me know what happened, and how can I avoid finding two shapefiles in totally different places?

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You're correct to set/change CRS definition of the layer because the layer does not come with a CRS definition. So best would be to find out (with the data provider) the correct CRS definition (maybe there is a description/metadata) in which the layer was created. Maybe the coordinate values could help with this.

If changing to EPSG:4326 macthes with the other layer, this is probably the correct definition. THe stripes you see could be an artefact from (internal, on the fly) reprojection. Zoom in to see if it disappears.

Also load a basemap in the background like XYZ tiles > OpenStreetMap to see if both layers are in the correct place.

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