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Thank you very much @ZJay07 for the PR
You are right in recognizing that ivy.sinc with tf backend throws an error but this looks like an ivy issue. Becaue the code in the actual implementation works with native tensorflow as in

import tensorflow as tf
x = tf.constant([1, 2, 3.], dtype=tf.bfloat16)
x = x*3.14
print(tf.cast(tf.where(x == 0, 1, tf.math.sin(x) / x), x.dtype))

which means it does support bfloat16 natively.
Are you able to figure out where our code creates an issue

seems like the right approach but now another test is failed due to this change

This is because the change is made in tensorflow backend, and when those two tests are ran with tensorflow backends they get value mismatches as you can see under "Combined Test Results".
NOTE: You will find the logs at https://github.com/unifyai/ivy/actions/runs/8513118977/job/23316369932?pr=28677.

sure