There are two questions here that must be asked first.
For example, the relationship with a government agency is not based on your organization's need for products and services but rather is required to obtain licensing, pay taxes, etc. Therefore it is out of scope. Yes, it should be included in your third-party inventory, but with only basic contact information collected.
With office supplies, it may fall out of scope because it is low spend and low risk. However, there may be SOME risks associated with the relationship. Suppose you purchase from a small local office supply store; you may want to run an OFAC report to confirm the owners are not on a sanctions list.
The most important concept here being out of scope means the normal TPRM processes do not apply. So, suppose there is a risk (even if it is low). In that case, you may want to re-evaluate if the third party should be back in scope and following due diligence for the appropriate risk level.
Those are my thoughts on the matter, but I would love to hear ideas from other members as well.