I noticed you didn’t mention the Roman senator’s recorded writings. Obviously he knew what was going on in Judea, and what Pilate was doing.
I defer to any classicist here or a classical philologist but Tacitus comments in his ‘Historia’ never seem to be questioned as they are contemptuously dismissive of Christians and rate Jesus as a subversive hedge preacher. He makes the comments in discussing Nero’s search for a plausible scapegoat for the fire that destroyed a good part of Rome during his reign. Since Tacitus is considered a hostile witness and he gets several major items at variance to the orthodox Christian teaching in his comments on Christians and Jesus his writings are not considered a possible later interpolation.