I believe the opposite: increased acceptance and adoption of Bitcoin by governments and large institutions leads to a rise in its price, not that a rise in price leads to increased adoption.
Unless there is more adoption by new companies and governments taking strategic reserves of Bitcoin, it's unlikely we'll see Bitcoin rise to new record prices like $150K and above. Reaching these numbers requires significant liquidity entering the market, and this is achieved through the entry of new companies and increased adoption.
But governments have only accepted and legalized bitcoin in recent years, and institutions have only entered the market since the ETF was approved. Meanwhile, Bitcoin has been around for years and has grown significantly before governments and institutions intervened.
So it can be both . As bitcoin became so popular and stopping it seemed impossible, governments had no choice but to adopt it to make it easier to manage. Meanwhile, bitcoin is unlikely to become popular globally without government approval and institutional push . Especially as bitcoin gets bigger and bigger, and if it wants to grow further, it needs more money to flow into the market , so there is no denying the role of governments and institutions in helping bitcoin reach $100k or when it becomes globally popular in the future.
Yes, Bitcoin existed before government approval, and it will continue to exist even if governments do not adopt it. Government adoption increases Bitcoin's spread and price, but banning or not adopting it by governments will not stop Bitcoin.
As for the role of a rising price in increasing government adoption, I don't believe it will, because governments are not concerned with Bitcoin's price, but rather with its reliability as a hedge against inflation, a reserve asset, and a long-term store of value.