At a basic level, how are mature organizations doing auditing of things like AD user accounts, inventory, etc?

For comparing users existing in the HR system to AD I would look to see if any automatic export tools are provided by the vendor. Take the dump of existing user information including a little information possible and write a powershell script to check for AD user objects and report back objects with discrepancies. If you could schedule an export or leverage an API to gather your HR systems data this could completely automated. Would perform a similar process with an export from whatever AV system you are using and instead user powershell to query the machines for whatever values you are looking for. This obviously would only work for things that were expected to be reachable. Typically orgs have tools for managing device configurations and software and leveraging them instead of rolling your own is likely best. There's tons of tools to make this process easier but there's a bunch of information we can't tell from your post.