BGP is tricky; you will not always have end to end reach-ability depending on how you advertise networks. Often you must use extended ping with source of IP that is advertised via BGP and exists on the destination router. and vice versa, destination router must have route back to source.
for example, we have R3 with 184.108.40.206 and R4 with 220.127.116.11; from R3 you must ping 18.104.22.168 source 22.214.171.124, if you do not, then router picks outgoing interface as source of ping whcih may or may not be advertised by router.
Try extended ping with source , if that fails, show us show ip bgp and do ping with source IP.
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