How do I reimburse myself after purchasing personal needs items for a relative in a nursing home?

I was my Moms POA and reimbursed myself by writing a check once a month from her acct. Her bank statement was my record. Showed the money going in and going out. I kept the receipts and placed them into an envelope with the month and the # of her check. This way if ever questioned I had back up. I don't see how you pay for her stuff matters unless for your own record. You still have to prove the purchases were for her. Medicaid never questioned my reimbursements, they we never more than $100 a month. I kept all this information until a couple of years back, Mom passed in 2017. I was also Executor. The beneficiaries are allowed to question at time the accounting is done. I was pretty sure my brothers wouldn't and they didn't but had the info if they needed to see it.

Keep meticulous records like Alva suggests, use a debit card like Geaton suggests, or use the POA to add yourself as an authorized user to LO credit card. Whatever you choose, just be sure to keep a very clear " chain of evidence".

My husband is PoA for his Mom in LTC. He uses her debit card to make purchases on her behalf.

Yes, but as with ALL THINGS being a POA you must create a file and have all proof available.
Let's take your example. The file would say "Expenditures for Month of May, 2022. In this would be your RECEIPT for personal items attached to a copy of the check you write yourself as POA on the account. This would hold true for ALL expenditures even if you hired someone to cut the grass at Mom's home.
Then at the end of May you do "May" for the file of "Monthly expenditures.
The May file will have all assets incoming listed whether pension or Social Security or anything else and it will also list all expenditure outgoing.
If you keep careful files and diaries you will be ready in court to defend at a second's notice what check was written when, to whom, and for what. You will have everything at your fingertips.
Treat each thing you do as someone suspicious is looking over your shoulder ready to call your actions and expenditures into question. Know you are prepared.
My files for my brother would have stood the test anywhere. And each Month he got a copy of every penny into his accounts and every penny out of them to put into his own file.
Good luck.
If you have questions about how to serve as POA then research the answers. That is easily done and you are doing A LEGAL duty, held to the highest responsibility as a Fiduciary.

Personally, I would pay with my credit card and send a check for mom's items directly to the credit card company.

This keeps your books clear of her items and leaves a precise paper trail of her legitimate expenditures.

Take or print a copy of the CC statement, highlight mom's items and staple the receipts to this with the check number, date and amount or even a copy.