Foundry USA basically works as any other pool - They have their own miners but you individual users can also join them in the efforts of mining bitcoin. The thing with Foundry is that they have amassed a huge base of miners, which allows them to currently have an astonishing hashrate of 248.8 EH/s[1]. They are actually part of a larger investment group called Digital Currency Group[2] - which also owns other companies such as CoinDesk.

I'm 99 % certain that this is not the real website of the company but instead a possible scam. A simple WBM search shows that the domain once hosted a cloud mining service[3] on October 2023 and shortly before the domain was on sale[4].
If you want to learn more about Foundry, this[5] is the source that you should visit.

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[1]https://mempool.space/mining/pool/foundryusa
[2]https://www.foundryusa.com/
[3]https://web.archive.org/web/20231206141536/https://foundryusa.com/
[4]https://web.archive.org/web/20220706221600/http://foundryusa.com/
[5]https://foundrydigital.com

The correct address is foundrydigital.com. Any other address that you're visiting is a scam.

The parent company (Digital Currency Group) is private and based in the US. They have to comply with US laws and regulations, though there is no crypto censorship related laws in place yet for the mining industry. Most allegations against Foundry is unfounded at the moment and they have not openly censored any transactions. So far, only MARA pool has openly declared that they're filtering non compliant blocks.

Agreed that Foundry probably has little to no government influence.
Just to iterate on your last point:
Donald Trump has stated that he hopes all of the future Bitcoin to be mined within the US. Would this statement still be positive for the crypto industry and what we stand for? In addition, would the recent stand that he takes still be positive for the Bitcoin mining industry in the US? Of course, discounting the fact that every one of them are just looking to rake it more profit.

Whether pro-crypto or not, they would still want to control most of the people's funds or portfolios. Maybe we shall stop hearing about bans or rumours of bans, but they will be pushing hard towards the regulation of the crypto industry.

With "regulation" they will now have a full say on how you mine, spend or trade your bitcoins among other things.

The USA can't control the BTC only what they have mined can they can control that, thanks to RickDeckard for an amazing research on the pool. BTW OP, why do you think this pool is owned by government officials or why this pool is trying to take control of the BTC or BTC mining? I mean, what paranoid thing you saw, I don't get it.

Is this actually possible? I mean, they won't know if someone is mining or not until they notice a consumption of energy in some place and wonder to check it. Why would a person be forced to join such a pool, just like people are not forced to use KYC exchanges now, as they can use DEXs too? (It will be optional.)