Yikes, what a mess! It's very hard to evaluate something like this. Take some time to cut out the junk and add your own good quality cord. 

Check out this YouTube short video from IFMGA certified guide Karsten Delap. (Yes, the webbing is tied directly through the bolt hangers, which is not standard practice, but still should not be direct cause for failure.)

Double fatality at Tahquitz Rock, CA, Sept 2022

When rappelling, both climbers apparently clipped in to a single loop of old tied webbing. The webbing broke. Both climbers fell and died. (It was raining, so perhaps the webbing was wet and harder to inspect or notice that it was old. The webbing was tested post-accident to only 2-3 kN. ) Here’s the accident report from the SAR team, well worth reading.

Sadly, I could go on, but I think you get the idea.

Webbing or cord on existing anchors is guilty until proven innocent! Always inspect it before you use it!

• Cord and webbing used in climbing is very strong and reliable when it’s new and tied correctly. But when it’s been in place for a while, subject to ultraviolet light, mountain weather, possible rockfall, and maybe nibbling by rock rodents, it can be dramatically compromised.

• A big rat’s nest of cord, with multiple slings ranging in age and quality, is hard to evaluate and potentially dangerous.

• Instead of adding one more piece of your own cord to the mess, do everybody a favor: cut out all the junk and leave just two or maybe three good quality pieces.

• Especially for more adventure climbing or alpine routes where you’re away from properly bolted anchors, it's good practice to bring some extra cord or webbing (and ideally a knife) that you can leave behind, so you know there's at least one good sling for your descent.

• My personal rule: I really try to avoid rapping off of a single piece of cord unless it’s something brand new that I just tied myself. Any single cord that I find gets a back up. (That might be a little conservative for some people, but we are all accountable for our own level of acceptable risk.)

• This is a fine reason to carry a cordelette. It's inexpensive and easy to cut up to leave behind when needed.

So, how bad is old webbing?

Short answer: it can be horrendously bad. My buddy Ryan Jenks at HowNOT2 tested some ancient sun bleached tubular webbing that was out in the elements for many years. It broke at about 3 1/2 kN! You could generate this with a decent bounce test when you're setting up a rappel!

Compare this to New 1 inch webbing which is about 18 kN, and 7 mm cord, which is about 13 kN.

Here's my cheap hardware store checkout line lock blade knife that I've had for like 20 years. It's taped securely shut so it can never accidentally open. It doesn't need to be fancy. It's been used countless times to clean up a rat nest rappel anchors.