Is the Fed an unconstitutional tax collector?

No, Congress has both the right to coin and the right to tax, and the Fed obeys federal law.

It is an important point. In 2015, the Fed could have given up the battle, let the excess reserves go funding government, and the fed keeps the Treasury portfolio indefinitely for seigniorage. The Fed could skip deposits all together and adjust seigniorage with buying and selling.  If it did, then, the tax bets reigns supreme, because tax policy determines seigniorage needed. The Fed has no direct mechanism to bet Congressional tax policy, which is highly erratic.

A taxing Fed is the same as a floored Fed, trying to operate as a single color channel.  The missing flow remains, but takes the long path, and the Fed ends up being the last to see it. The Fed is simply reduced to maintaining traction with Treasury.