My cat is addicted to bath water, but it makes her start choking...?

Had my first cat for about a month now. I have had some concerns about the amount she is eating, but a routine check at the vets says she's put on weight. I have always placed 2 fresh bowls of water, one in a normal bowl and one in an upright which refills itself and away from the food.

A few days ago, as she's exploring more she's now started just sitting in my bath. I made the mistake of running the water a little and now she is addicted. Everytime I go to the toilet she rushes past me, sits there, cried and licks what I can only assume is a limescale filled tap (I only have showers)

At first she gulped loads down but immediately started choking and nearly being sick. So I thought had too much too soon. However she is STILL desperate for more. Earlier I did a little and she only took 2 sips but was regurgitating about 10 times.

Can anyone explain the reasons, solutions and maybe reassure me that there isn't an issue....? She has fresh bowls and surely choking isn't exactly great.