As described in the RFC, Padding DNS packets is useful only when the DNS traffic is encrypted (Otherwise, it just increases message sizes at not additional value). Therefore, implementation of the EDNS(0) Padding Option is limited to protocols which encrypt DNS messages during transport (such as DNS over TLS or DNS over DTLS).
Sinodun runs a project to create proof-of-concept level implementations of DNS over TLS. Their project plan contains EDNS0 Padding as a Key Implementation Feature. They also keep a table of implementations.
The Padding Option is implemented in the following DNS servers/clients/utilities: