How can I tell what this PR budget claim actually means?

Start with the underlying figures, not just the headline. Check which years are being compared, whether the amount is approved funding or money actually spent, and which agencies or activities are included. A large total can be misleading if the scope changed between years.

Even if the comparison checks out, a budget figure by itself does not show that particular messages are coordinated, effective, or intended to distract from another subject. Those are separate claims that need separate evidence.

Also, “public relations” and “propaganda” aren’t interchangeable labels. Government communications can include outreach, public information, or advocacy. To judge what’s happening, look at the actual material and who funded or distributed it, rather than treating a spending figure as proof of what audiences will see.