If Jennifer is the one who "unofficially" dumped Mariner, and Jennifer wants the dumping to be official, then Jennifer should have made it official by talking to Mariner.

The reason Jennifer doesn't is that she realises she was wrong to dump Mariner and it would be cruel to go talk to Mariner just to dump her again. Which doesn't make it Mariner's responsibility! Jennifer regretting her bad actions doesn't mean Mariner owes her anything. And sexually harassing your ex isn't better than the alternative.

The episode even lampshades the fact that Jennifer clearly dumped Mariner by having Mariner say so. Her friends point out that can't be true if Jennifer still thinks they're in a relationship. Which is a valid point made moot by the reveal Jennifer was lying. So yes, Jennifer is clearly the dumper.

Ultimately this comes down to Jennifer being unhappy that she chose to dump Mariner without actually talking. Which is a problem Jennifer is entirely responsible for. Mariner was trying to have a straightforward conversation when she got dumped. She was talking about her feelings and asking to be treated with honesty and dignity. Jennifer flatly refused.