"So I am wondering if this srr-queue bandwidth could have influence on iperf3?"
Possibly.
The 2960 series doesn't have lots of buffer RAM and QoS, on that switch, can often compound the effect of the lack of buffer RAM.
Interfaces and/or QoS stats showing drops?
Another possibility, not mutually exclusive with the above, if you egress bursts above 20 Mbps, your ISP might be dropping traffic too, and if doing enough of that, throughput can be very much reduced.
Iperf stats show packet loss?