Is it better to make my mom a dependent or put her on disability?

As someone explained to me on this forum SS disability is not based on income. It would not hurt to talk to a Social Security lawyer. He would be the one to help you apply. Mom will get Medicare with this.

How old is Mom? If she is a widow, she can collect SS at 60, 62 at 75%. For her to be a dependent on your income taxes you must be paying for 50% or more of her care.

You are quite confused and using some terms incorrectly. SSI is not Social Security Income...it means Supplemental Security Income. SSI is for poor people (old, blind or disabled) and a person with a million dollars in assets does not qualify. Social Security is an earned benefit that has no interest in your assets or other income. If she claims Social Security early based on disability go for it. Or just wait till she's old enough to get Social Security retirement benefits. Medicare kicks in at age 65 OR if someone has been on Social Security Disability Insurance (SSDI) for 24 months. Doesn't she already have medical insurance? Definitely get good legal and financial advice because you are going to need it

She has enough assets to pay privatly. If she is under 65 then she can apply for disability and Medical insurance depending on her current low income, even with assets. If she is 62, she can apply at a lower payment. Keep in mind that early onset dementia tends to have deterioration more rapidly than an older person so waiting to 100% may be moot.

Remember she has a lot of assets. You can get her into a nice memory care where she should not be bored if she did nothing at home. And at 27 you need to work to build your own financial security.The problem is if you can get her to sign documents making you POA. A good elder attorney can assess the client if it is still possible or if you need guardianship/ conservatorship.. Bring all documents with you including her retirement statements. Each state has different laws.
Do not make her a dependent. Someone will be able to post the reasons. You can find a certified elder attorney in your area www.naela.org or www.nelf.org

These are questions for an Elder Law attorney who can help guide you. You'll eventually need to discuss her finances and financial strategies with a financial advisor but that can come once you've gotten some advice on the legal issues and powers of attorneys, guardianship, etc. Don't do anything without some guidance from an expert because those decisions could have consequences both for you and for your mom. It's good that she currently has resources to pay for care right now so you have some time to figure things out. But, your first step needs to be to interview a couple of Elder Law attorneys and establish a good relationship because this is going to be a long road for you both. So sorry.