Slow Service Possible Tree in Line of Sight
While satellite service has drastically improved over the years, the latency inherent to satellite internet remains unchanged. Streaming is possible with satellite internet but it is subject to many variables that can slow down the experience, such as latency, congestion, internet traffic, network optimisation strategies, the streaming services themselves and how they react to latency, and others. So, while streaming works, it's not guaranteed and people's experiences with it vary enormously.
Regarding games, while turn-based games work with satellite internet, real time games don't, due to latency. For more information, see https://www.hughesnet.com/frequently-asked-questions
Also keep in mind that all the people and devices connected to your wifi will use data, which can be used very quickly (especially by streaming). You will need to keep an eye on the data so you don't run out.
If by "power users" you mean a lot of streaming and other data intensive activities, HughesNet may not be the right service for you, as it's not really designed for cord cutting or cord cutting like activity. Streaming in HD can use upwards 3GB or more per hour, depending on the streaming service. Even with a 50GB plan, that's still only ~16 hours of streaming per month, and with everything else done via HughesNet using data, even that ~16 hours isn't at all realistic. With SD it tends to range from about 700MB to 1MB per hour, again depending on the service.
What the tech told you about streaming isn't necessarily true, though with congestion being higher than normal right now due to so many more people being home and on the service, and coupled with that congestion the high latency inherent to geostationary satellite internet, streaming can be difficult at times.
Fortnite will almost assuredly not work properly. The average latency of 600 - 650ms makes it practically impossible to play real time online games, unfortunately.
Regarding the slowdown after the tech left, though I don't know when they were there, it's possible that it coincided with the start of the late afternoon/early evening slowdown that often occurs due to that being the time when the highest number of people are online.
The existing cable being reused by the tech should be fine. If they were to see anything iffy with that cable they would have likely replaced it.
