A used Fender Blues Junior gets you close.
A used Fender Blues Junior or a Roland JC-40 will get you 90% of the way there for under $400.
Julia Jacklin’s clean tone is basically a Fender Twin Reverb turned up just enough to get that slight edge. The Twin is loud, heavy, and expensive. The Blues Junior is the practical alternative: smaller, cheaper, and still does that Fender chime. It takes pedals well, which matters because she uses a bit of reverb and an occasional tremolo.
If you want something even cleaner (no tube breakup at all), the Roland JC-40 is the secret weapon. That solid-state clean is absurdly sparkly, and the built-in chorus is exactly what she uses on tracks like “Body.” You can find them used for $300-$400.
Skip the cheap modeling amps for this. A Fender Mustang or a Boss Katana can do a lot of sounds, but that specific clean chime isn’t one of them. You’ll spend more time tweaking than playing.
Used Blues Junior is the move.