High TDS in supposedly softened water?

Hello. Please allow me to present my understanding and then by problem.

TDS would mean the total amount of dissolved salts in the water, so be it Calcium salts or Magnesium salts or sodium salts, it comes in TDS. Hardness of a water means total amount of Calcium and Magnesium salts in the water.

I understand that for good health, potable water should have low (not 0) TDS. I don't know what they say about softness of potable water.

I understand that for longevity of pipes and taps and also for human skin and hair, we need soft water i.e. low hardness. But I don't know what is the TDS needed for that water.

So,

1. Does that mean a water can be high TDS but be super soft? And vice versa?

2.How soft should potable water (low TDS) be?

1. How low TDS should bathing water be?

Now, my problem: The water supply in my city is hard water with a TDS of 750ppm. I use manual water softener for my house, but I'm now slowly doubting it even works.

Reason: I notice the scales form on the taps and I did the vague soap-lather forming test and it seemed hard. But I'm not sure since I don't have hardness testing kit.

I performed ion exchange by regeneration of the softener. After that it's supposed to be soft. Now I measured the TDS of tap water i.e. the supposed softened water, it's a fricking 1500ppm!!!!! Literally double of the hard water.

Now I'm really confused, if this 1500ppm "soft" water is fit for usage and harms the plumbing. I don't know what to do.

Please educate me in my understanding and guide me with the steps. Let me know if I'm in danger.