Your mother named you as her "attorney in fact" in her General Durable Power of Attorney. Your first question is whether you should be listed on a checking account with
her only as her attorney-in-fact; you are concerned that your assets might become liable for some obligation of your mother because you are now listed on her accounts.
I think that you do not need to worry. I can't be absolutely sure because I don't know how you are listed on your mother's checking accounts. I suspect that you both hold the account in joint tenancy. Legally, either of the owner of an account in joint tenancy can spend any of the money in that account.
If the account is in joint tenancy, I very much doubt if any of your own assets could be held responsible for some obligation for some obligation of your mother's. I can't be 100% sure, because I don't know what state you and your mother live in. It's remotely possible that your state has some weird law about joint tenancy that extends liability for joint owners. I can say that I've never heard of such a law. Generally, shared joint ownership does not make either owner liable for obligations of the other (beyond whatever assets in held in the joint tenancy account.)
Also, I wonder how likely it is that your mother will "become embroiled in a lawsuit or some other legal issue" My instinct is that it's highly unlikely. If I'm correct, what seems important is that you continue to pay her bills for her.
I think that you are now acting acting as your mother's agent-in-fact for her financial matters. However, that issue is controlled by what her durable power of attorney states. What does it provide regarding when you can act as your mother's attorney-in-fact? This may be a moot issue. If you continue to pay her bills from the joint account, (ie that account has sufficient funds so you can do so), your bill paying is not under authority of the DPA, but under your rights as a joint owner of the bank account.
I'll conclude with a general observation: there is too much fear about possible lawsuits in this country. Certainly no one want to get caught up a a lawsuit. But it's important to try to evaluate how likely that is, rather than to decide that any possibility at all of a lawsuit, no matter how infinitesimal, must automatically outweigh all other concerns.