I don't think it's really relevant here whether PlayStation is a walled garden or not. As other commenters have pointed out, Sony would have been paying Twitter

I don't think it's really relevant here whether PlayStation is a walled garden or not. As other commenters have pointed out, Sony would have been paying Twitter for API access in order to provide this service to customers and they have no control over Twitter changing pricing or TOS - which was probably the reason for this feature going away. Sony not giving you a way to easily extract your own data from the system is a consequence of it being a walled garden, but there's no onus on Sony to integrate specifically with other arbitrary third parties.