What do you consider table stakes for a well run IT procurement process? If you were coming in to assess the state of your IT procurement processes - what would signal to you that it's efficient and effective?

Having short times from need to procurement that consistently select the correct vendor that can deliver on budget and on time.

I would look for the following to begin with, and go from there according to the level of maturity you are expecting.
1. I am able to bucket the vendors into 3 tiers : primary, secondary, tertiary. And the teams are aware of who are in this groups. From my experience having them bucketed saves the IT leader from half of the issues especially in an environment with little to no procurement process.
2. There is a strong co ordination among the VMO, PMO, legal(compliance) and IT leadership.
3. There is a process defined to onboard or renew a vendor
4. The costs associated are tracked through few systems and have system of records and not in some random excel sheets.

My table stakes for a well-run IT procurement process would be knowledge of all IT licenses, contract details, duration, support components, internal ownership by department, and working notes from previous negotiations.  The ability to validate usage, user/device counts, true-up or true-down ability, usage rationalization and retirement, and competitive environment.  A yearly schedule of all license renewals and the associated budgeting commitments.  End-of-Life or End-of-Service knowledge for operating systems, databases and applications plus patching details.

The table stakes for a well-run IT procurement process, should include a collaborative approach across the organization (key stakeholders) to identify business needs and establish a proven/reliable list of suppliers to strategically source goods and services and can acquire on short timelines.  Establish a process in place to perform evaluations on supplier performance to ensure high quality products are obtained at an advantageous term. And finally, use metrics to track and analyze purchasing activities.

Consistency, Procees, coordination across various teams