Modifying your render distance with the slider in video settings doesn't actually change how many chunks you see when in a multiplayer game (1.16.1)

This isn't a bug? You have to change the render distance in the servers .properties file.. If the server is set at 10 you will only see 10 chunks.

playing on an external server limits the rendering distance to the one set by the server owner. If the server's server.propreties file, as quoted above, is set to 10 which is the default, you will be able to set your render distance to anything between 2 and 10, but setting it above will not show any other chunks.

I have a doubt regarding this issue, if the server is limited to 10 chunks and the client has for example 16 render chunks, the chunks 10-16 could not be cached on the client just for rendering.
I don't know if there is any mod that does this or if it can be implemented in sodium but it sure is a very useful feature

The feature request for chunk caching is tracked in issue #149 .
It's unclear whether this and issue 270 mentioned above are an invalid bug report or duplicate feature request, but either way these issues should be closed. If you'd like to discuss this or get tech support regarding this, please consider joining the Discord server.