I have the same stuck on „Checking for Updates“ problem with just a little over 200 GB of add-ons on XBox Series X. Maybe the 500 GB limit is an additional issue, but the symptoms are the same. It is working fine right now with 187 add-ons installed, but when I install more it stops working once I hit a limit. The limit seems to depend on not just the number of add-ons, but also the number of „subpackages“ within the add-ons. I have all world updates installed and right now my add-on limit seems to be 190. When I installed the world updates last, I got to about 210 before it broke. The world updates have lots of „subpackages“ (files/folders?).
I used a cloud sessions to uninstall add-ons. If you uninstall an add-on in the cloud, it also gets removed on the XBox. Normally I find that quite annoying but right now it allows me to „fix“ my XBox, when I have hit the add-on limit again, by installing and then removing an add-on in the cloud to reduce the number of installed add-ons on my XBox. It saves me from having to start from scratch. Downloading everything takes a while.
I hope this will be fixed soon. In two weeks there will be another world update and it probably will push the add-on limit even further down. I already have lots of planes that aren‘t installed.