Not really. Your wallet address needs to be shared with others if you want to transfer money, and anyone that knows your wallet knows all of your transactions. If Google decided to build a crypto wallet into Chrome, I think you can agree it would trivial for them to see all of everyone's transactions.
I agree that BTC has terrible privacy. But this is a BTC problem, not a Bitcoin problem. A smart Bitcoin wallet would not reuse addresses across transactions, and would split your coins into many fragments, making them virtually impossible to trace. But to do this you need low fees and therefore big blocks - what BSV and BCH are doing. Several wallets on BSV already do this today, like HandCash (https://handcash.io), and the user experience is fantastic.
In case anyone reading this is as confused as I was: there is a schism in the cryptocurrency world where two forks of bitcoin, known as BCH and BSV, both still claiming to be bitcoin-but-not-that-other-bitcoin (BTC, the token meant by 99.9% of people who say "bitcoin"), have decided that their pope is the only authentic one.
Close. Bitcoin is a concept for a system - described in a whitepaper and in forum posts, and expressed in an initial release. BTC would prefer you think they alone are Bitcoin, but is the Catholic Church alone Christianity? Certainly not. BTC, BCH, and BSV are all implementations of that idea, each with various degrees of similarity to the original Bitcoin, and each of which share a history back to the genesis block. Interestingly, when you dive in, you'll see that BTC is the one that has diverged the furthest from the project's original goals and protocol, not the so-called "forks" BCH and BSV, which were both created from not wanting to change protocol rules. This is good reading if this viewpoint is new: https://thatsbtcnotbitcoin.com
Almost any online transaction today (in the US, at least) involves a credit card or PayPal, either of which divulges your name and maybe location to the merchant. Bitcoin doesn't.
I don't know what to make of your strawman about Google. This thread was asking about problems Bitcoin solves. Bitcoin allows payments without an intermediary automatically divulging your identity to the other party to the transaction. It doesn't also need to end the arms race of consumer privacy in tech in order to be a useful advance for privacy.