the switch doesn't officially have a browser.
however it does have one to enable access to public wifis
people noticed this and used a trick with the dns to open this browser and use it for "web browsing"
however i am pretty sure it can't download files, the 3ds browser didn't allow download of files as well (i think you could save pictures but that was it)
search in the internet "how to access nintendo switch browser" you will find millions of results
HO wait, you are asking for a "homebrew" browser?
there is no homebrew on the switch. neither hack, no cfw etc.. and don't ask when there will be one, because no one knows.