McDonald’s and Starbucks are grassroots boycotts. On the BDS webpage they state that HP, Siemens, AXA and Puma are primary targets, as well as fruits & vegetables.

Regarding these boycott lists that exist in the internet they write

The global nature of today’s economy means that there are thousands of companies that have links to Israel and are complicit to various degrees in Israel’s violations of international law. However, for our movement to have real impact we need our consumer boycotts to be easy to explain, have wide appeal and the potential for success. That’s why globally, while we call for divestment from all companies implicated in Israel’s human rights violations, we focus our boycott campaigns on a select few strategic targets. We also encourage the principle of context sensitivity, whereby activists in any given context decide what best to target and how, in line with BDS guidelines. There is a lot of information online claiming that some large companies give money to Israel, some of which turns out to be false. BDS has built a reputation for strictly adhering to established facts and producing the most accurate information.

Google would obviously seem like a relevant target given this explanation and their current targets. At the same time, I can also only imagine that it would be more about pressuring companies to move away from GCP and pressuring Google to stop the collaboration with the occupation.