tfd.Categorical.log_prob returns wrong dtype

In tfd.Categorical, the log_prob method derives its return type from the logits (or probs) constructor argument, as in the following:

logits32 = tf.constant([1,2,3,4], dtype=tf.float32)
tfd.Categorical(logits=logits).log_prob(2).dtype == tf.float32 # True

logits64 = tf.constant([1,2,3,4], dtype=tf.float64)
tfd.Categorical(logits=logits).log_prob(2).dtype == tf.float64 # True

However, if a list (batch) of [logits] is supplied, an unexpected type demotion occurs such that the return value of log_prob defaults tf.float32:

logits64 = tf.constant([1,2,3,4], dtype=tf.float64)
tfd.Categorical(logits=[logits]).log_prob(2).dtype == tf.float64 # False

Start at tfd.Categorical.log_prob and reproduce the reported dtype difference between a direct float64 logits tensor and a one-element list containing it. Trace how the batched constructor argument determines the return dtype, then add a regression test showing that the list form preserves float64 and run the relevant Categorical tests.