In the UK there is an explicit exception to copyright for the purpose of time shifting:
Details of the exceptions to copyright that allow limited use of copyright works without the permission of the copyright owner.
A recording of a broadcast can be made in domestic premises for private and domestic use to enable it to be viewed or listened to at a more convenient time.
While many streaming services allow one to watch any content at any time, some for example Pluto TV do not, and presumably base their business model on people not doing so, perhaps so people do not time shift past the adverts. However it is pretty trivially easy to record the provided video, I tested it with the instruction here and the process is pretty analogous to the old days when one would do this with a tape based video recorder which I assume was the use case that prompted the exception. There are no terms of service that one explicitly agrees to to get to the video feed.
Is it legal to record Star Trek Discovery from Pluto TV at friday 9pm (the only place/time it is available in Europe AIUI) and watch it on saturday, then delete the recording?