I suspect this is actually where things are going wrong (there’s “no sparklyr available” because install.packages() can’t even access the repo). Note that if you check the PACKAGES URL that it’s failing to access, there’s definitely an entry for sparklyr.
This problem is often the result of proxies, firewalls, or other traffic filtering software blocking R from accessing remote URLs, so maybe start by looking into how your system is set up on that front?