Does the second icon, "Network Connection:etho:avahi error" look like the attached? If you right-click it and select 'About,' does it say Network Monitor 2.28.1?
It is simply a monitor icon; it does not assist or prevent connection. It simply indicates if you are connected. You don't really need both this and Network Manager.
The part about eth0:avahi error is simply telling you that there is no cable attached and we couldn't get an IP address.
You may safely right-click it and select 'Remove from panel.' You don't need both. Solved?
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