You know your situation better than any of us and your biggest asset right now is having a solid head on your shoulders - major kudos to you for keeping that during a jarring, life altering event.

When there are no assets and no children, a legal battle is never worth it. It’ll just land you in debt. Yes a lawyer may sell you some vague hope but lawyers aren’t exactly neutral when it comes to telling you whether you one and it is common for the legal fees to exceed the monetary award in a divorce, meaning your networth is worse off having pursued “justice” with a lawyer than if you’d just let her go. She has no assets. You have no kids. One month’s worth of living expenses - even six months worth of alimony - the legal fees could easily exceed whatever you hope to be awarded.

You can file in small claims court for her share of the lease rent without mucking up your divorce with it or getting lawyers involved. That’s a separate contract and is easier/cheaper to resolve on your own.