Okay, but this shows that they made massive acquisition in 2020 (presumably at the bottom of the market in response to COVID) and are now unwinding

How much of that is shares as opposed to treasuries, MBS etc?

When the Fed purchases bonds, that reduces interest rates, and lower rates make asset prices go up.

The Fed purchases the bonds with cash created out of thin air with a journal entry. That newly created cash is used by private actors to purchase assets, which makes asset prices go up.

The Fed could purchase equities directly, but it doesn't have to own them to influence their prices.

But that again applies to all assets, not just equities.