Running tcpdump on an interface/SVI only shows the traffic destined to the switch itself to be processed by the control plane. In order to capture the data plane traffic, you could try the following:
1. Port mirroring
Mirroring traffic to a port destined towards a collector/monitoring device
2. Advanced mirroring to the CPU
On the 7150/7500E/7500R/7280E/7280R, we can run port mirroring on an interface and send one copy of the dataplane traffic to the CPU where the tcpdump utility can be used:
[Section: 188.8.131.52 Filtered Mirroring to CPU]
We also support Sampled mirroring
If the connections you wish to investigate are the data flows going through the switch then sFlow, is the feature you are looking for. Once configured on the switch using the guide in the following link https://www.arista.com/en/um-eos/eos-section-44-1-sflow-conceptual-overview#ww1152186 the switch will send statistics regarding the traffic flows which should allow you to have a good understanding of what kind of connections are going through the system.
However, if by connections you mean the connections to the switch control plane(eg. who is logged into the switch right now), you can use the who command and you will get a list of users logged into the unit:
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