Is black tea a pH indicator?
The colour of black tea is given by a complex mixture of theaflavins and thearubigins.

These compounds are formed by enzymatic oxidation and condensation of polyphenols of green tea, typically of gallocatechin and epigallocatechin gallate ( EGCG )

Basic dissociated forms of these compounds have strong absorption of visible light due to delocalization of phenolate electrons. This absorption  decreases a lot when phenolates are protonized in acidic environment.

So yes, in some sense, black tea infusion is a $\mathrm{pH}$ indicator, similar to litmus or juice from red beet roots. Many natural colourful compounds have $\mathrm{pH}$ dependent colour, as their molecules undergo acid-basic reactions.

But synthetic indicators are better due stability, sharper and better defined colour transition.