I suspect one of my siblings is using Mom's credit and has credit cards in her name. How can I do a credit check to confirm this?

annualcreditreport.com

For the time being they're offering weekly credit checks (instead of yearly) because of COVID

You could always freeze her credit to prevent additional credit being taken out in her name. You're given a password to unfreeze it, and if you lose it, you're out of luck.

I froze my mom's credit after my dad died, because I was handling all her finances myself and she'd have had no need for credit. I took out a credit card in my own name and paid her bills with that, knowing there was plenty of money to do so.

If mom's CG is paid with funds from Medicaid(whatever it is in your state), then the care all needs to be provided to her. However, CG likely to report that she only cares for mom, not your brother.
Geaton 777 is correct in describing the one way you can request credit checks in your mother's name. If she is unwilling to do this or if you are not able to spend time alone with her to make this phone call, that may be an indicator of concern about her care/your brother's motives...or it could be an elder who has chosen her son as her primary care manager. One child usually does end up with the task.
APS would need an indication of some sort of current harm or risk of severe injury/death in order to actually investigate. Reports can be filed on lots of concerns, but often do not meet the standard for investigation.
Elders have a right to privacy and self determination....and to make poor decisions...just like all adults in US.

What in the world do you think a credit check would show? The more cards are used the better the credit is.
Are you POA? If so you can register this with all the three credit agencies and you can run credit checks for your Mother. If you are NOT POA you have no rights to dabble in the credit information of others.
The POA may be added to her card to make purchases for her. If you suspect your brother of fraud take your evidence to APS and ask them to investigate for elder fraud. Your brother is allowed to access your Mother's funds for your Mother's needs and care if he is in charge of caring for her.
Why should your Mother not do laundry. An elder LIKES to keep busy and contribute to the running of a household. When I was an RN the one way to make the women happy was to allow them to help fold things.
This sounds like sibling wars to me, which always makes me very unhappy and very sad for the parent in the middle of it.
Again, if you suspect fraud tell your bro to get his papers ready (assuming he is POA) for a visit from APS as you don't trust him.

So what is the evidence of financial abuse that is causing you to be suspicious? You won't legally be able to do a credit check if you're not the PoA but will need to present evidence to an lawyer or APS.

None of your info or profile says your mother has dementia. If she's got all her mind (even if she has a poor memory) then his PoA authority is not active unless he has Durable PoA. Hopefully the PoA document doesn't allow him to make loans "on her behalf".

If she has her mind then you can make a call to a credit agency with her present and together on speaker phone may be able to get the info she needs as she gives permission for you to join in on the call.