Resurfacing a concrete birdbath is very easy! All you will need is a bag of leveling concrete. Or any concrete that you have lying around the house.
The less water you put in the concrete mix, the thicker the concrete. The faster it will dry. I used more water to slow down the drying process. So that I could work with the concrete in stages. To spread it around in all of the holes in the birdbath.
Let the birdbath cure for a few days before you put water in it.
This concrete is smooth without pebbles or rocks in it. This is the only size bag that they have, 50 lbs;
https://www.homedepot.com/p/Rapid-Set-50-lb-CTS-Indoor-Outdoor-Self-Leveling-Concrete-Underlayment-186010050/204414391