What you are missing in the previous question you linked is that Japanese leaders always hoped for a negotiated settlement to the war which would allow them to keep some things they wanted.

By the time of the Soviet invasion, what they hoped to keep had been severely reduced. More like securing the Emperor's position in a conditional surrender rather than holding on to a sizeable empire. But they thought they could still negotiate somewhat with the threat of mass casualties from an home island invasion as a bargaining chip. The Soviet invasion and rapid advance (combined with the nuclear bomb strikes) made it psychologically clear to (some of) them that their bargaining chip held no power over the allies. Their perceived options went from conditional surrender or (American) invasion to unconditional surrender, (Soviet) invasion or potential destruction in a psychologically shocking, short time frame.

So while the objective hopelessness of their situation may not have changed that much, their perceived best option did.