Providers may also deprioritize home Internet traffic before they do mobile phone traffic during times of high usage/congestion. They do install additional equipment/frequencies in areas where they are providing home Internet services, rather than just adding those users to the towers and existing bandwidth that were already in use for mobile phones, but like every ISP they do oversubscribe, and it's a lot harder to go beyond a certain total.
It's completely impossible to predict your speed because it depends on where the tower is located that you'd connect to, and where you can place the equipment, and what the terrain, trees and buildings between you and the tower are like. My sister has AT&T 5G home Internet and gets about 100Mbps (and my nephew does game on it happily, but he's not a "competitive gamer" so a little latency in things like a first person shooter or MOBA don't bother him), but 5G latency isn't completely awful. But she had to put the gateway in one specific corner of the house to get that connection, because phone service with every provider sucks inside her house.
Most of those gateways provide antenna connections, so you could set those up in a good position, like in an attic or even outside the house to get better signal, and run the cables to the gateway. I don't really think a "better" third-party gateway will make any difference in speeds, but there may be additional features you like. (Or simply known issues with the ones provided by T-Mobile that you want to avoid.) Keep in mind you'll be under carrier-grade NAT with 5G Internet, just like a mobile phone, so you won't have your own public IP address and can't do things like port forwarding.
300Mbps would be at the very high end of what T-Mobile or any provider will let a user get most of the time, because that's a LOT of bandwidth taken up and cuts into the margins on the service and affects other users. They could throw tons of backhaul bandwidth in going to the tower, but there's just a hard limit on how much they can spread around a given area via the wireless part, and adding a new frequency band or adding a tower to reduce the area of coverage is a high cost. There might be periods where you get higher, as T-Mobile says "typical" speed is 133-415, especially if you're lucky enough to be in an area that is not heavily oversubscribed and doesn't have a lot of mobile users, but that could change over time as more people use 5G; T-Mobile won't do anything to increase available bandwidth until the service has reached a point that it's unacceptably slow for users. But you simply can't tell without testing, and even testing with your phone may not represent what a 5G gateway would get.
A "hotspot" service from a wireless provider is intended to be mobile. You can take the little device anywhere and it's basically just a cell phone without a screen, with very limited "router" features. That is often used by people who need Internet service where they couldn't get anything wired or don't need it permanently, like a construction company office on-site at a job or as your friend used it. They price that service high for the convenience of mobility, usually with low data caps and reductions to 4G speeds during high congestion. 5G Internet is similar but is intended to be in a fixed location, and is priced to get people who want service in one place, at home (not a business). Taking it somewhere else violates the terms and could be detected if you take it too far away because it will be trying to connect to towers you couldn't normally reach. They don't seem to actually enforce that limit in most cases, but those devices aren't as portable as a "hotspot" device.
The 5G Home Internet service has limits that most wired services don't, like all wireless services. You'll be deprioritized during congestion, and get even slower if you go over 1.2TB per month. They also control your streaming video resolution like mobile phone service does (depending on "available speeds", whatever that means).
T-Mobile does give you 15 days to test the service, so you won't just be stuck with it. Just keep your current service active until you decide. Personally I'd still pay a good bit more for wired service like fiber or cable. I'd check how that works if you don't have any other T-Mobile service, since the terms say it comes by "bill credit" up to two billing cycles after you submit the request. Last time I had a credit with a cable provider after cancelling, they sent me a pre-paid card.