etcd 3.5 health endpoint not usable when authentication is enabled

[tdolphin]

Cannot query 127.0.01:2739/health when auth enabled in version 3.5
Steps to reproduce:

❯ ./etcdctl endpoint health
127.0.0.1:2379 is healthy: successfully committed proposal: took = 6.168636ms
❯ ./etcdctl user add root:passw0rd
User root created
❯ ./etcdctl user grant-role root root
Role root is granted to user root
❯ ./etcdctl auth enable
Authentication Enabled
❯ ./etcdctl endpoint health

{"level":"warn","ts":1624550312.4325728,"logger":"client","caller":"v3/retry_interceptor.go:62","msg":"retrying of unary invoker failed","target":"etcd-endpoints://0xc00014a700/#initially=[127.0.0.1:2379]","attempt":0,"error":"rpc error: code = InvalidArgument desc = etcdserver: user name is empty"}

127.0.0.1:2379 is unhealthy: failed to commit proposal: etcdserver: user name is empty
Error: unhealthy cluster

GET request to gateway doesn't give expected result

❯ etcdctl --user root:passw0rd auth disable
Authentication Disabled
❯ ./etcdctl endpoint health
127.0.0.1:2379 is healthy: successfully committed proposal: took = 2.579161ms

Expected: GET 127.0.0.1:2739/health would still work after authentication is enabled without requiring authentication.
Actual: errors giving unhealthy.
This means http GET cannot be used any more as liveness probe.

Note that:

etcdctl --user root:passw0rd endpoint health
127.0.0.1:2379 is healthy: successfully committed proposal: took = 22.706843ms

[tangcong]

thanks @tdolphin. pr #13145 will fix it.