Google has never done a blanket X% cut across the company (perceived or otherwise) to my knowledge.
Google has made changes in the past that have resulted in layoffs (or whatever term you want to use). Office closures have happened. Orgs have been merged / relocated.
Google nearly always offers affected employees a way to stay at the company - they might not be feasible for everyone but the options are clearly communicated. I don't have numbers but office closures tend to result in higher numbers of departures due to relocation not being viable for those tied to a particular city.
Google have lots of financial knobs they can tune to avoid layoffs. Everything from reducing the number of food offerings on site to terminating contractors that work on areas that will need less investment / support during a downturn. Outsourced work (using vendor teams) is something that can be ramped up and down faster than employee counts and with less visibility. You downsize something like geo verification and literally no googlers would notice as the vendors teams are in other locations away from normal Google offices.
Google has been super disciplined with managing spend for years now. It's really clear from earnings calls how they are managing spend and staying profitable. Even when things suck in the economy they're beating the market's expectations. And I'm not surprised, they probably have one of the best sources for how the economy is doing. Search and ads data provides an amazing level of insight to consumer confidence.