Ok, now it is getting kind of strange. Mainly because it does not matter if the F5 is configured for offloading or passthrough...
So, this is at least how I would continue here:
Check the details of a tls handshake from your F5 and also from a connection directly to a server
Compare these TLS handshakes
Do a packet capture on the firewall towards your F5 and the server which is not locatdd behind the firewall
Compare the TLS handshakes
If there is still no obvious reason in the handshakes you need to dig deeper: start a packet capture with also logging enabled and enable the features proxy basic and flow basic. During connection tests for connecrions towards your F5 check the global counters multiple times. Maybe there is already something. If not then aggregate the captured logs and analyze them, at latest there hopefully is the reason why the connection towards your F5 isn't working. (Probably this could be analyzed on the F5 also, but there I have no idea how it works as I never used such a loadbalancer/WAF)
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