Not sure if they could formally charge TS with her murder if his DNA was found on her body but it would be a step in the right direction.
Depends on if TS claims they dropped her off somewhere. If his claim can be collaborated by witnesses or by other means, the presence of semen indicates that sexual relations took place but doesn't prove that TS is the murderer.
If a dead woman's body is found on her own bed in her own home and semen can be linked to the last man she was with, especially if a stranger's semen is found, then that's pretty damning evidence. Let's say, Jaren had sexual relations with her bf prior to going to work and his semen is found, that's not proof that he harmed her because it makes sense that they could have had sex earlier in the day.
They'd have to link her back to their hotel room or have witnesses say that they were seen out together before LE could conclude the person who left the semen behind is the killer.
By the way, do peeps routinely have unprotected sex with random people these days? I mean, would TS even do that? Would Jaren?
Wouldn't he know, if he intended on killing her, that his DNA would link him directly to her body?
Unless he thinks, because he's made so many bodies disappear before, that her's wasn't going to surface.