Electronic – Is SMPS a non-isolated power supply

Completely isolating the controller from both primary and secondary sounds strange.
Here are the common approaches.

Controller on the primary side. The secondary side is isolated. The output power flows through the transformer. The feedback signal is brought back to the controller on the primary side. Typically, an opto-isolator used to bring the feedback signal back to the controller across the isolation barrier.

Controller on the secondary side. The half-bridge remains, of course, on the primary side. Since both output voltage and controller are on the secondary side, the feedback signal doesn't need to cross the isolation barrier. However, the gate control signals need to cross the isolation barrier from the controller to the Half-bridge. Gate-drive transformers or opto-couplers are used for that. The controller also needs an auxiliary power supply be able to start up.

Block diagrams taken from: http://powerelectronics.com . The block diagrams show flyback converters, rather than half-bridge. But, they still represent the isolation schemes.

Sure they have transformers: -

The transformer looks different to a regular AC type but it's still the largest single component on the PCB but a whole lot smaller than it would be for 50/60 Hz operation. The transformer is the big yellow taped thing in front of the heat sink at the back/left.

SMPSs also use opto-isolators for feeding back a measure of the output voltage so that it can be regulated. This is another significant isolation feature thus, output and input remain galvanically isolated to several kV and are therefore "safe".