As PPs have said, she doesn’t stop you. You stop yourself.
This is obviously not typical behaviour for a 24 year old. Most have either left home or can’t wait for parents to be away. Many have children of their own.
You seem worried about her, as you mention she’s mentally unstable. Why does she ask you not to leave her? What’s she worried about? Does she work? Did she live away at uni and how did she manage then? Do you have another adult child who lives with you and could support her while you’re away?
There’s always a solution. If she needs your emotional support, then you could arrange to video call at a particular time each day, at a similar time to when she usually chats to you at home. If she wouldn’t manage to cook properly for herself, you could batch cook with her before you go or go shopping with her to buy ready meals. Could one of your neighbours pop in to check she’s OK. Or a friend who lives locally?
It really depends on how bad she is and how worried you are. But if her anxiety’s so bad she doesn’t want to ever be apart from you, that’s pretty serious and she should be taking steps to get help to manage the anxiety. Has she seen the GP about it? There are lots of techniques or she may prefer medication.
Why do you call her a monster? Were you being flippant or do you genuinely feel that. Is it possible you’re not recognising a potential disability? Could it be she’s neurodivergent and that’s why her anxiety’s worse. If so, it’s important you take it seriously. You need to help her get to the bottom of her behaviour.
Bad anxiety can be terrifying and debilitating. But, whatever the underlying cause, she needs help managing it and becoming independent. You’re doing her no favours if you let her rely on you too much, as she needs to build a life of her own.
If she copes fine and is being self-indulgent, then obviously just go away.