The mains transformer input MUST NOT be connected to GNDA.
The mains transformer current should circulate between live and neutral.
The mains side safety ground is just that, for safety. It should not be used for normally carrying current. It carries current if the live to ground insulation is breached in the transformer, and blows a fuse, pops a breaker, or operates a GFCI device.
Once the wiring of the mains input side has been sorted out, then the negative rail of the DC side may be connected to mains safety ground or not, at your discretion.
A larger safety concern is whether the mains transformer actually is connected to neutral, and it's been mis-labelled ground, on the basis that neutral is '0 volts anyway!' Usually, the neutral conductor is 0 V, when the mains distribution is wired correctly, and supplied through a correctly wired polarised plug. Mis-wirings are not uncommon, and if the supply comes through a non-polarised 2-pin plug, which are common in every country in the world, then it's a 50-50 chance whether your 'neutral' wire is roughly ground, or live.