I have the same problem. Watching on Windows 10 laptop on google chrome with good internet speeds. It starts well and then it's like it runs out of energy. Spoils the whole experience. It's got to the stage that I am cancelling subscription. This performance from a communications Company is unacceptable. BT take no responsibility but they are the one I pay.
I use the Discovery + app on an LG TV to watch rugby on TNT Sports and at times it's impossible to watch due to the stuttering. Using the BT Sports app was fine.
We are customers of BT and pay for a service from them. If BT chooses to outsource their service to a 3rd party provider that's their choice. If that service is unacceptable it's up to BT, who we pay, to fix the issue. BT must have a Service Level Agreement with Discovery+/TNT Sports, which seems obviously not being reached, by the number of compaints on the BT community about this. I renewed my contract with BT partly to be able to watch the rugby. I am now commited to a contract that provides me with an inferior service. Trying to pass the buck is unacceptable.