Google doesn't release net income numbers by business unit but in 2021 revenue for search was around $148B and Youtube revenue was around $29B. Given that youtube revenue dollars are probably much more expensive than search revenue dollars I'd say that ratio will skew toward more of the profit being in the search category than the you tube category, not less. It does seem on balance to be a relatively small part of their business dollars-wise, although I'd make the case that the cultural relevancy that youtube gives google has a non-zero value.
They don't break out the profitability of some subunits, but according to the WSJ it was "breakeven"[1] in 2014 with $4B in revenue.
I still don't see where the GP comment's confidence that it's not meaningfully profitable comes from. It doesn't seem like an uncontroversial assumption that costs have more than septupled in the last five years in the way that revenue has.
Citation needed... Is $7B/quarter not a lot of money?