Check `eos_newton_tol` for non-ideal EOS and different floating-point types, e.g., `Float32`.

Right now, the default values of `eos_newton_tol(eos)` are typically set for `Float64`, e.g., `= 1e-8`. We should check which values make sense for other floating-point types such as `Float32`. See https://github.com/trixi-framework/Trixi.jl/pull/3079#discussion_r3513009300

Start by locating the eos_newton_tol(eos) definitions and read the linked discussion in PR #3079. Compare the current defaults for non-ideal EOS implementations across floating-point types such as Float64 and Float32. Done means the appropriate tolerances are determined for the supported types and the relevant behavior is checked.

Written by the indexing model from the issue text.