Tim Anderson isn't going to just get better at Shortstop by osmosis. Omar would actually have to be a good teacher, which is something we have absolutely no idea about.
Being historically good at something <> being good at teaching something. It more often means the exact opposite.
Fun Fact: Ron Washington had the same exact same career fielding percentage at shortstop as Tim Anderson
Signing Mookie Betts after not trading for him is the absolute best thing you can do to win a title in 21 or 22, trading for Mookie Betts and not signing is pretty close to the worst.
I think the MUCH more likely scenario is trade for him, lose the division anyway, have him walk the next off season, and regret giving up whoever it is.
Mookie Betts has won a world series and is generally beloved in Boston and still wants absolutely zero to do with an early extension. Let's get the idea that having him here for a year will make him more amicable out of our head.
Here's an idea, Trade for Haniger AND sign Corey Dickerson. Dickerson is your primary DH, and spells Eloy and Haniger when necessary or take over left if Eloy continues to be a disaster. Leaves plenty of cash to throw at pitching.