A number theory problem by Syed Hamza Khalid

There is a 2 digit number which can be written as $\overline{xy}$ where $x < y, \text{ and } y = x + 1$ . However, when $\overline{xy}$ is squared, it results in a number $\overline{abcd}$ , where digits may be repeated.

What is the maximum number of repetitions of a certain digit in $\overline{abcd}$ ?

BONUS : Do more than one set of numbers exist to qualify as $\overline{xy}$ with the above features?