For me, the only definition that anybody cares about is whether the governance of the overall system is controlled by a government or not.
The governance in what sense? In terms of the network, it is decentralized. The government cannot force you to run a set of rules you don't agree with. You will simply swap those gov-coins for bitcoin. And if government makes mining illegal, or tries to censor the on-chain transactions, then that gives a high incentive for another country to claim that extra value, and it's where the miners will go.
Yes, the US government can't force you to do anything with your keys, and you're free to use your keys on whatever fork might be out there.
The US government
can, for instance, decide which fork may be legally called "Bitcoin" since the government is the one who enforces trademarks. In practicality, a fork that was not sanctioned, or even at odds with the US government (e.g. being blocked at all possible off-ramps, etc.) would be nearly worthless to trade, especially if there was a competing, fully-sanctioned, legally named, "Bitcoin".
And in all practicality, miners will go where the money is--especially since most have very large stakes in BTC themselves. By holding the price of the asset hostage, the US government could make miners and every other stakeholder in the network do whatever they wanted.
Trump does not have the power to control all miners scattered all over the world. If world leaders make efforts to unite just to control Bitcoin, only then will we see how rebellious people can be when they strongly oppose something.
The bottom line is, it is impossible and very unlikely for the government, no matter how powerful, to control all of Bitcoin's mining processes and totally eliminate other miners.
Nobody needs to control that, they just need to control the price and hold that hostage over Bitcoin holders. The US easily has the power to do that. If people have to decide between "purity" and their BTC still being worth something, I know what 99% would choose...
Influencing the price of Bitcoin is different from controlling it.
Not really. Almost all holders of BTC are in it for
the money. If BTC holders are faced with losing almost all of their investment, they will do whatever they need to do.
Over the years, governments have tried to ban Bitcoin, restrict its usage, sponsor attacks against it through the media, and also make the environment difficult for Bitcoin to thrive through unfavorable regulations, but they have not been able to stop Bitcoin usage or how people adopt it. This is because all of those actions only have a temporary effect on the price of Bitcoin, but not on the entire Bitcoin network.
If Trump can successfully alter the design of the Bitcoin network and how the network operates (not just the price), starting from mining, node operations, etc., then we can say Trump is actually controlling Bitcoin.
Trump and his party in Congress could pass laws that would have the effect of altering the design of the network, etc. by, for instance, saying that you cannot use the trademark "Bitcoin" unless it's the codebase they approve of. They could do it many other ways too--it's not like the government itself would be mining or running nodes or something since that's not necessary.
To be realistic here, the only reason this would happen today is that Trump somehow figured out that it would help him make more money (say he wanted to donate Satoshi's coins to himself and his friends). This probably won't happen since Trump has other ways he's making money (he made $1.7 billion this week

), but you can also imagine Trump and his party going out of power and a new regime wanting to do something different.
In any case, the answer to the OP is: yes.