Should I connect all power supply ground together?

As above. I'm just unsure if it's safe to connect the ground if the 2nd diagram to ground if the first diagram (which are basically the transformer secondaries).

So I got 2x of this supply. (2 separate transformers with dual secondaries each. The 2 wires from the 2 secondaries were connected to make center tap)

Screenshot_20231120_001037_Chrome.jpg


And 2x of this supply. (1 transformer with dual secondaries. 1 secondary for each bridged rectifier)
IMG_0056.jpeg

Thanks in advance.
 
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So I got 2x of this supply. (2 separate transformers)

That diagram has only one secondary winding which is center-tapped. It uses a bridge rectifier to produce two output voltages.

And 2x of this supply. (1 transformer with dual secondaries)

That diagram has only one secondary, and no ground point is shown for it (we would need to know what point you want to ground). It uses a bridge rectifier to produce one output voltage.

Thus, the diagrams and your descriptions taken together don't completely make sense. Can you be more clear about what you have and what you want to do?
 
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In that case the grounds can be connected together.

There might be a question of whether they are also connected to chassis ground, AC power line ground, etc. Normally chassis ground is connected to AC line ground for safety. Low voltage power supply circuit ground may sometimes be tied to chassis ground through a "hum breaker" circuit.

There may also be a question as to where the grounds physically get tied together, say, tie them together at the power supplies, or tie them at the load.