That was a later program. You're misunderstanding because he used the word "stimulus". There were multiple rounds. The first, was a huge corporate giveaway.
The first one was .4% the size of the cares act and it was for healthcare, not corporate giveaways:
More than $3 billion for "research and development of vaccines, as well as therapeutics and diagnostics"
$2.2 billion "in public health funding to aid in prevention, preparedness and response efforts — including $950 million to support state and local agencies"
Almost $1 billion for "medical supplies, health-care preparedness, Community Health Centers and medical surge capacity"
You are correct. The original commenter was incorrect in the assertion of the order of the bills "passing" - "it didn't even take a week before the government passed the largest stimulus ever".
Granted the one you reference was passed prior, the CARE Act was introduced first. The CARE Act was never in danger of being dropped, as the market was counting on it (it is filled with pork).
They announced their intention but I don't believe they have actually bought any yet [0, 1]. Also, their balance sheet shows they are buying predominately U.S. Treasury securities and Mortgage-backed securities [2].