I am my mom's POA. She resides in a LTC facility. Is it necessary to send POA documents to Medicare and her other health ins. (supplement)?

Well, likely too late on some levels if she has dementia. I was POA for my brother per his request when he was diagnosed with early Lewy's and moved to assisted living, asking me to take over paying all bills, including supplemental, getting all records from his supplemental insurance, keeping files on everything and etc. What a job. The Medicare and Social Security required his permission to send any documents to me, including what portion of hospital bills were paid by medicare. So did his supplemental insurance and his credit cards. I had to sign that I was responsible for telling the credit card companies, as his POA, if his mental acuity was not good enough to manage the cards I was getting in my mail and paying as his POA. EACH ENTITY will have their own rules and will be glad to tell you about it as long as you are glad enough to hold online for one to two hours. It was a mess getting things set up. Start with the banks, to be certain you are on the account as POA so that you sign correctly on the checks, her name, with you as POA. After a year I got it all together pretty well with the occ. glitch of Spectrum turning off his phone for no good reason and etc. We were at opposite ends of our state. What a trip that all was. I sure do wish you good luck.
Do know that medicare will send you documents if you Mom agrees, but SS is different in that if you are not prepresentative payee (two doctor letters that Mom is no longer competent and all the other papers as well as yearly documentation, SS will do little for you. IRS is a whole other barrel of monkeys and I stress monkeys.

If you’re helping a family member or friend with a Medicare claim or appeal, your loved one will need to fill out an Appointment of Representative form (in addition to the POA document), which authorizes you to legally represent him or her in Medicare decisions. This form should be sent to the same organization handling your loved one’s Medicare claim or appeal. If you have questions about this form or aren’t sure where to submit it, call 1-800-MEDICARE (1-800-633-4227), 24 hours a day, seven days a week; for TTY assistance, call 1-877-486-2048. If your loved one is enrolled in a Medicare Advantage or Medicare prescription drug plan, he or she will need to contact the Medicare plan.

https://www.ehealthmedicare.com/blog/caregiver/power-of-attorney-for-family/.

I don't believe it is required. However, if you need to communicate directly with Medicare or with the insurance supplement company, they will require the POA document. And I'm not sure if the POA document alone would suffice for Medicare as they also have their own form(s). Medicare has an "authorization to disclose information" form that I remember my husband had to sign to allow me to act on his behalf for Medicare when he was in rehab, even though we each have POA for the other. Even if you have no need to be in touch with either outfit now, it can't hurt to get the POA document, and other needed forms, on file with them. I assume you have the POA in your mother's records at the LTC facility. You also want to make sure that any correspondence from Medicare or the insurance supplement comes to your mother at your address rather than being sent to her at the LTC facility. Same for social security correspondence.