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In the paper "Soft Actor-Critic Algorithms and Applications", appendix C shows enforcing action bounds using the tanh squashing function which is in (-1, 1). I have action bounds in (0, 1), so can I just modify the tanh output by applying the following transformation: output = 0.5 * (tanh_output + 1). If so, do I need to change logprob formula too?

I have not seen any SAC implementation with different action bounds other than the paper's (-1, 1).

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Yes you can map the output onto [0,1] as you indicate. You should treat this as a modification to the environment. I.e. imagine that the environment takes actions in [-1, 1] instead of [0,1]. No you don't need to change any equations.

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