No, I don't think " economic growth is purely about money in circulation" and no economist would make that claim. That would be ridiculous.
Other than the mischaracterization of what I think, I can almost agree with what you've written in the above paragraph which I quoted. However there is still a key misunderstanding on your part. I suggest you start calling the government debt the "deficit". That will help you keep your thinking clear. The concept of debt, as you personally know it, does not exist for a government that is the source of it's own sovereign, fiat currency. Instead you should think in terms of the amount of money created by government and spent into the economy minus the amount of money taxed back out of the economy. That difference , if it is positive, is the deficit. If it's negative it is the surplus. The government's difficult job if to balance the deficits and surpluses against the need for money in the economy. Your conception of "shrink[ing] the 'government debt' as a percentage of GDP without having to repay anything" is stemming from a misconception that the government has debt. The government, yours and mine, does not have debt.* It has deficits. The deficits can be too small or two large depending on how well they balance with the needs of the economy.
By growing GDP without increasing the deficit proportionally one can reduce excess deficit. The government can also do this with a correctly focused tax increase. And a third way of doing this temporarily also exists. And that is by substituting Treasury liabilities for excess outside money, i.e., selling sovereign bonds. These three methods are not perfect equivalents however.
Your confusion partly stems from your belief that governments borrow deficits by selling bonds. Although this does have the appearance of borrowing, it is actually something quite different. Think of sovereign bond selling into the private sector as the temporary sidetracking of excess money in the economy by substituting future treasury liabilities, and you will be on the right track. Thus sovereign bonds are a tools of Central Banks. They also serve the important purpose of being an interest paying temporary store of money that otherwise would lose buying power due to inflation.
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*I am aware that politicians regularly refer to "government debt" . They have no better understanding of fiat money than you.