The tracert equivalent that I use would be traceroute or mtr. If you can get a response from the gateway and access the server locally, it would indicate an IP routing issue as local subnet traffic is working.
Instead of pinging a domain name, what happens if you ping a public IP like Google DNS (8.8.8.8)? The error you're seeing could be related to a DNS resolution issue although that should not affect access to your server.
Are you able to access the server's Linux shell via KVM or out-of-band management during the Internet outage? If so, I would first check the kernel log for any errors. I'd then follow up with a PING to the local gateway within the same IP subnet to validate Ethernet connectivity. After that I'd start performing PINGs and traceroutes to subnets beyond the local gateway to see what's going on with tcpdump capturing all interface traffic in the background.
This is what I use but with Debian. I had an older NUC 8 i5 lying around so I decided to drop 32GB of RAM and a new 1TB NVME drive into it. The performance is way better than a Pi and the measured power consumption at the wall socket is under 5 watts idle (peaks at around 13-15 watts under load if I recall correctly).
In terms of noise level, if I start loading the CPU heavily the fan can be noticeable .. however at idle or when it's just streaming Plex content to my TV (without transcoding), it doesn't make any fan noises at all.