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> There is no effect on money supply if this is funded through taxes

Of course there is. Suppose we tax Elon several billion dollars. Now, instead of sitting in his money vault, it flows into the economy where it increases demand pressure.

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He doesn't have a money vault. He has almost zero cash holdings. If you tax him, then he will have to sell assets to pay for those taxes, which removes money from the economy as that money was being actively spent on his assets. The only situation when money supply changes is if someone has a literal mattress full of cash hidden away. Even if you just have money in a savings account, it acts as a fractional reserve for the banking system meaning that there is a net decrease in money supply when you give it to the government as banks can no longer use it as the backing for loans.

To split hairs slightly that is the "velocity of money" (basically how often does the average dollar get spent and passed around per year). Money supply is the total amount of (a given type of) money in existence. But yeah, the effect on inflation is the same.

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