does pausing a keyword actually stop the spend or does it just move

Both are true, and which one applies depends on whether the campaign is budget constrained. If it hits its daily budget every day, then removing a keyword frees that money and it goes to whatever else can absorb it. Your total is flat by definition, because the budget was the binding constraint, not the keywords. Whether you gained depends entirely on whether what took the money is better than what you cut - usually it is, but that's worth verifying rather than assuming. If the campaign is not budget constrained, the spend genuinely disappears and the total should fall. That it did not is worth a look on its own. So: not theatre, but on a capped campaign it is reallocation rather than saving. Measure it as conversions per pound, not as pounds spent.