As Ralf noted, padic numbers need special support to read/write. For some reason (maybe bug) this support is not active when using normal files.
Well, should it be active? Now that you showed what I discussed in my answer mail (thanks a lot for this demonstration -- I should add it to the help section of FriCAS), I guess we should make it work, since it is a really cool feature to be able to save and load potentially infinity objects.
Actually, now I understand why File saves lisp expression and not the OutputForm.
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