Hm, yes internet
does work with Basilisk II.
If you enable slirp in the Basilisk II GUI and set TCP/IP to Ethernet and DHCP you may connect to some server.
There are obstacles however.
There is no even half recent browser for 68k Macs.
We had a modem those days and Deck´s AltaVista was our search engine. (The greybeards do recall)
You may try a 68k version of iCab though, the oldies are still online: http://www.icab.de/download.html
Even if you can find a HTTP page, it will look very strange compared to what it should look like.
HTTPS was not there when we used the old Macs, so no app from yonder will know how to handle that.
FTP should work, but many such servers were moved into a HTTPS container, afaik.
For a HTTP example, this is Macintoshgarden.org rendered by iCab in MacOS 8.1:
Guess you get the idea, why WWW is not really recommendable with MacOS 8.1.
A text only browser may be worth a thought, if you are content with that.
You might set up a Hotline client instead too to connect to a server.
Best of luck anyway!
Sorry to tell that the Android build of Basilisk II does not seem to connect as in the example above.
Its a known issue, that some features do not work as expected with Basilisk II Android.
Not sure whether its a build issue or a problem with my tablet, though.
Forgot about a discussion in 2016 over at Macintoshgarden.
User m68k also reported that Basilisk II Android did not connect to a network via TCP/IP with SLIRP enabled.
We may conclude the Android build is incomplete regarding network, methinks.