That's is not how inflation works and how fed works.
Fed controls the inflation rate by raising interest rates. When it raises interest rates by 2% only , the whole world takes money out of any high risk asset (such as gold silver stocks or bitcoin etf) and buy bonds.
If fed wants to fuel the economy, it just decrease the rates and everyone put their money back to economy and risk assets.
Fed doesn't need to buy bitcoin to control inflation at all
That's why they need tools to make debt without worry about inflation.
Yes they need gold and btc no wonder why the fed allowing the btc to existing.