If the TODA for the runway was greater than or equal to the TODR from your performance calculations, then you are "guaranteed" to get airborne,
Depending on the rules applicable to the certification, TODR will have up to half or two thirds the airborne distance to screen beyond the end TORR. This is to give you some comfort that the aircraft should be airborne by the end of TORR. Guarantee ? pretty likely but prefer not to figure in guarantees ...
before the start of the (rising) obstacle surface at the end of the clearway.
No warranty that the clearway won't have some slope associated with it ...
It all depends on your first and second segment performance and the slope of the obstacle surfaces over which you are flying.
Which is why it is prudent to consider first segment gradient and ground slope in the relevant part of the takeoff.
Sounds like this is just a reproduction of FAR25
Pretty much the case. 20.7.1B originally was the operational recasting of the Australian certification requirements. ANO 100.5 reflected the BCAR while 100.6 FAR 25 - both now well and truly binned post Ron Yeats' involvement.
and is essentially just a requirement that the aircraft doesn't sink while the gear retracts.
That's the certification line in the sand.
Runway slope is a factor for takeoff, but not climb. Obstacles in the departure splay must of course be taken into account, but this has nothing to do with runway slope.
As a general consideration, that is a reasonable position. However, for those aircraft which have an abysmal first segment performance, takeoff over rising ground (doesn't matter whether it is the runway or beyond the runway head) warrants some risk management going a little bit beyond just applying the AFM requirements.