the government is not going to be buying btc on the public markets en-bulk. they will be doing private trades with other institutional investors.
notice how ETF sponsors dont use coinbases public exchange but they trade on a separate private coinbase "prime" separate market which doesnt affect the public market

the public market is where price discovery happens(sets the price), but the private 'prime' market just exchanges according to the public market price without affecting the public market
so dont expect big 1k-10k-100k buys in one day on the public market to shoot the price up.

secondly when the governments of countries or their individual states hoard coin. they can then collateralise it and then offer things like bonds to its citizens. this will then give normal people a way to invest in "bitcoin price exposure" without needing to hold bitcoin themselves(like etfs did). which is where normal people then dont actually need to buy from the proper bitcoin public markets. again not helping the bitcoin price growth
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remember how the ETF didnt help with the bitcoin price. the bitcoin strategic reserves wont either.

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all we can hope is that governments dont regulate citizen access to not be able to access public market exchanges of bitcoin to force people into only being able to invest in bitcoin etf/bonds of treasuries/institutions

the main positive of government investment of btc is the mindset that bitcoin is a legitimate asset. its like giving it a gold star rating⭐ a green tick ✓ legitimacy