This is not a paradox and not even confusing if you pay careful attention.

From Sleeping Beauty's perspective, two of the potential outcomes are 100% correlated with each other: waking up on Monday with tails and waking up on Tuesday with tails. She can't observe the correlation, but she knows it's there because of the setup of the problem.

Of course you don't assign separate outcomes to two things that are completely correlated!

If SB gets points every time she makes a correct guess, then she has a 50% chance of getting two points if her policy is to guess "tails". In that case, guess tails: her expected payoff is 1 point. If she guesses heads, her expected payoff is a half point. (If she guesses randomly whenever she wakes up, her expected payoff is 3/4 of a point.)

Otherwise, it it's 50/50 and doesn't matter. For instance, if SB is killed (at the end of the whole thing) if she's guessed wrong, she may as well guess randomly.

If you are a dissociated consciousness and are teleported uniformly at random into a just-woken SB, breaking the correlation structure, of course you should guess that you got teleported into the tails branch.

It's just a cautionary tale to not ignore the correlation structure of your problem, and to get your payoff metric right. No paradox and--are people seriously even confused about this? It seems an awfully straightforward application of dependent events.

(Everything about the problem becomes clearer if you change it so that if it's tails, she'll be put to sleep and woken up every day for a year. "It was tails" lets her be right 365 times but only wrong once, but if she's going to be killed at the end of it all, "tails" is no better a strategy than "heads".)