It's good to hear from novice cyclists because that means more people are taking up cycling.
And more can question the antics of the tin can only brigade.
Yet another opinion. In the OP example I would stop if I were going to continue cycling along road, but not if I were proceeding to the cycle path as stopping does not benefit any traffic.
Edit to add:- scanning streetview further it looks as though that cycle path leads straight to the next ASL box allowing cyclists to easily bypass a queue of cars for Morrisons. If so that must be a plus for using it at busy times.
However scanning around this junction using Streetview I am utterly confused, by the whole junction both for motor traffic and cyclists; the markings seem absolutely bizarre. Do those who painted the road markings have any idea how to interpret them?
I am also confused by the large ASL boxes; how are they meant to be used? If you want to turn right do you cycle on the left and then cut to the right in the box.
However these are not unique in this respect though.
Another oddity is that traffic from Duke Street to the A5097 seems to need to turn right against a direction arrow. The markings all seem to be new as well as one Streetview shot showed faded markings, so a new lot of money has been spent.
I would think whether to cycle past the red light into cycle lane is a minor issue here.