Q.Bougainvillea
Pink bougainvillea flowers are turning to a grey-like colour. Not sure if that is a sign of over or under-watering?

It is difficult to say, without seeing an image of the plant.
Greying of the blossom color could be due to aging of the flowers.
Browning of blossoms could be due to watering issues, disease, lack of sun or other environmental issues.
Soil should be well draining and the roots should never sit in soggy soil.
Here are some links with care information that may help you pinpoint the issue.
https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-in-containers.htm
https://www.gardeningknowhow.com/ornamental/vines/bougainvillea/bougainvillea-garden-care.htm