Combine 9V and 1.5V power supplies to make a 7.5V supply

A typical use of the power supply schematic in the O.P. is for powering one (1) analog circuit, which needs both positive and negative power supply rails. In principle, you can power two (2) completely independent circuits from it (+9 to 0 and 0 to -9). This would be a peculiar scheme, though, because the ground of one circuit is at 9V (plus or minus) w.r.t. ground of the other one. Still, if the circuits are in fact independent, such scheme would work. In practice, this scheme is not used in general purpose desktop power supplies.

A classic desktop power supply (like the one in the YouTube video linked in the O.P.) is of a "dual positive type". Each channel has its own independent secondary winding (or even a separate transformer) and its own rectifier. The channels can float with respect to each-other, and that allows to connect them in series.

It is very likely that there will be no problem connecting them in parallel, as long as you can get the Voltages close to equal. A few mV will probably not matter. It is unlikely that current will flow into the output of the lower voltage supply unless it is the type of supply specifically designed to operate in this fashion (e.g, Hameg).

You could try asking the manufacturer about your question, although if it is "fake" then that might not matter. Also, you could consider renting a beefy supply just for this project.

Not all supplies can be put in series. It depends on whether they are isolated from Earth ground. Yours probably can be put in series, because it has green jacks (for "Earth" ground.)

Good luck to you.