I'm sorry this is happening, OP. As a divorced person with a child who has divorced parents who split when I was an adult (thankfully they had the wisdom not to pull this bs with me), this is how I'd handle it. Honestly, I'd be really angry and unable to mask it. I'd probably say something like, "Mom/Dad, WHAT THE HELL. You don't get to put me in the middle of this just because I'm now an adult. Have some boundaries. Dump this on me again, and I'm hanging up!"

This is how it is, OP. If it's any consolation, you have plenty of company. FYI it gets even harder. Instead of them taking care of each other, you will be taking care of both of them, in separate locations. Being an adult child of divorce is a lot of responsibility and sometimes horrifyingly expensive. Lots of travel.

You might want to check if they've updated their wills and powers of attorney. If they are both single when they have their first health crises, you will be dealing with it.

Well, if it's any consolation to you OP, my parents didn't divorce and they still put us kids (and now the grandkids) in the middle of their fights. So sick of it!

I don't have specific advice other than to clearly state to both that you know they don't want to put you in the middle and that this type of complaining does just that. My parents divorced when I was in my mid twenties and it got very ugly and really threw me for a loop for a few years. It's gotten better but my dad just retired and now is starting proceedings to request an adjustment to alimony...so it feels like round two is starting.

Hugs to OP and others going through this.