Finances and passwords, oh my! How do I handle this?

If it were me I wouldn't trust her with passwords. Put as many bills on auto BillPay as possible and tell your mom you're doing this for timeliness and convenience (which you are), and give your mom monthly printouts for her banking acct, investments, etc. That's what I do with my mom. If she wants to see it on the computer, do it for her.

Can you setup the accounts with a permission that she can look, but not touch? My bank recently added the feature and I see where it would be helpful in situations similar to yours.

Put a password app (I use Fastpass but there are others) on her computer. The passwords are encrypted and automatically filled in when she goes to the website. Make sure any "change my password" requests get routed to your email.

You can set things up so that she doesn't need to know the passwords to log in and so that she can't change passwords. Use a password manager so that the passwords are automatically filled in. There are third party apps for this but most browsers have this functionality built in. Most browsers have it defaulted to be on. I always turn it off. It's that pop-up that asks if you want the browser to remember a password. Use that and she won't need to know the passwords to log in. Just make sure you keep the machine that remembers the passwords secure. Set a master password to unlock the saved passwords if she can handle that.

As for keeping her from messing up the passwords, URL block the page for each site to change the passwords. Then she won't be able to mess them up.

I had to double-check I didn't write this because I am dealing with the same exact thing with my mother. I also want to hide her passwords from my father because he can't be trusted.

IMO it's just not practical or safe to continue to allow LOs with memory issues or compromised decision-making abilities to manage their online accounts. If they change a password and then don't update it in the app it can make such a mess. I use 1Password and I think LOs would be confused or misunderstand some of the messages that pop up on their computers.

I think telling them a therapeutic fib, like: the latest system update has bugs, or the latest system update isn't working with their computer, is acceptable. My 90-yo mom occasionally asks me for a smart phone (she has never used anything but a flip) -- nope, sorry. I still work full time and can't be her on-call tech help! About 5 years ago I set her up with a very inexpensive tablet that I've loaded with games and added a subscription to Lumosity. She really enjoys that but still struggles to understand "what happened" when she accidentally puts her finger on something and what she was doing disappears. There is a service called Last Pass that stores and releases passwords after someone dies (that they have set up in advance). I've not used it but am going to check it out (for my husband!!)

We went through this with my mom. It was a very frustrating period of time so I feel for you! On the one hand I was trying to protect her self esteem and feelings for wanting to keep doing things herself, but on the other hand we had to keep her accounts available to us. What we did was simplify things (move things to autopay) tell a lot of therapeutic fibs, and sympathize with her. We tried auto filling passwords, we tried taping a list to the computer...but it all boiled down to the fact she had no business doing her accounts anymore, and actually just plain struggled with using the keyboard and basic commands.
And still, nothing we did has made it any easier for my mom to accept that she has lost the ability to use her computer the way she always has. It's another part of her independence being chipped away by her dementia. She still says it's 'broken'. She still says she just needs someone to 'show her again, and she'll remember', and she still says there's strangers (her daughters) using her computer and messing it up so she can't use it, fueling her natural need to be suspicious.
In hindsight, I wish we had just removed the computer, saying we needed to get it fixed. We just prolonged her and our frustration. She didn't really use it for anything except pictures. She didn't get anything but junk email, which can be a safety issue for seniors anyway. It depends on what your mom uses the computer for, and if you can replace it with a tablet or something. My mom was basically just downloading a crossword every day, and she doesn't do those anymore.
My mom has always been paranoid about her money. Since I was going everyday I would print out her account snapshot statement. I taped a message on her computer telling her that all her bills were being paid on time. But this does not end the problems you are experiencing. She has, over many months, eventually stopped asking about it as much, and has said in lucid moments that she knows she needs help with those kinds of things. I try to help her focus on what she can still do not what she can't.
Moving my mom out of her house soon and frankly glad to be done talking about the computer. It became as big an issue as not being able to drive the car.
Best wishes whatever you decide!

Check LastPass, it will automatically fill the passwords. https://www.lastpass.com/ You can give yourself administrative access and you will always have access.

The real concern is not the password but 1st mis paying the bills or some how opening her self up for theft.

I pay my moms bills, and take screen shots of the page showing the balance or bills to be paid and email them to her. After her checks arrive in the beginning of the month- I send that screen shot,. It took about 2 months for mom to trust me and give up the angst of trying to log on and do it herself. Her first priority was seeing her new money in the account, getting the bills paid was second. I have the utilities on auto pay- those bills arrive at her house, The rest arrive at my house now. Mom now has more time for fun- she joined the local senior group and does things with them- I never thought I would see that day. She is 88.

Tell her to hire an accountant if she doesn’t want to allow you to handle it.

You are showing her everything while you are present. Why does she have a need to look at it when you aren’t there?