Homemade broth! Seriously, people overthink this!!! It's simple food preservation 101, not rocket science you know.
You're looking at 3-4 days MAX in the fridge, definitely not longer or you'll have issues. If you want it to last, get it into airtight containers and deep freeze it. I've got my Bosch freezer packed with stuff, lasts for months that way, practically forever!!! No faffing about with weird smells or questionable bits floating in it. Just good common sense, like wiring a new plug! Always label your containers too, its a lifesaver.