Home internet and Samsung TV keeps disconnecting

If you did not default the network settings on the TV prior to joining it to the T-Mobile network you might do that. I cannot say for sure as the network adapter wireless frequency the Samsung uses might be important to know. The specification for the TV should probably include the wireless version and authentication type it can use. It might depend on the age of the TV and if it is WI-FI 6 802.11ax capable or maybe WI-FI 5, 802.11ac or earlier. If it is earlier you might need to add an additional SSID on either the 2.4GHz frequency or the 5GHz with the authentication type it needs. If it does not play well with the 802.11ax due to the more advanced features such as band steering that might account for it dropping off the network. Knowing the network capability of the TV network adapter will help. Also you could probably check with the Samsung support site and get help there. I would guess by now other Samsung owners with T-Mobile gateways have connected with them to ask the same question.