Hello Eloise, welcome to the site.
Given what I can see through your window and since you are growing them inside, I would think you do not live anywhere where it gets very hot for long periods of time even in summer, and by that I mean 95+F/mid-high-30s C for weeks at a time. So once per week was probably a little generous. The main rule with watering these plants is to water thoroughly when the soil is dry, and not just dry at the surface but dry deeper in the pot. However, from what I can see from the plant, the base pad does not show any signs of rot, so while it may have been overwatered, it was not so bad that it really started the plant rotting.
On the other hand it is not uncommon for Prickly Pears to get a little floppy when seasons change and they are not actively growing. If you have not watered them in a while I would see what a good watering would do for them. Also since they are indoors, I assume it never really gets that cold and since they were still getting light, barely watering them for 6 months might have been a little long. Your soil looks pretty good in terms of growing a cactus, but before you water, check if it is really dry deeper down - there are cheap water meters available (even IKEA has some, but I am not sure how well they would work with cacti), but if you do not have one some times pushing a bamboo skewer down can give you a sense if the soil is wet or not. If all else fails working a finger down into the soil a good bit can also give you a sense.
Then if you do water give them a good drench, but avoid having standing water in the dish under the pot (maybe let the pots drain in the sink or in a tub), then see how they respond to that and only water again when the soil is about dried out.
Generally Opuntia are pretty forgiving of mistreatment, the ones I have killed have been following two scenarios: for one reason or other having a plant sit in a thoroughly wet pot for weeks at a time when it is winter cold (which is not really that cold compared to most places) or the opposite when I forget to water plants that were barely rooted because I was propagating them, for weeks at a time when it is very hot (so summers here).
If it came to the worst case scenario and the section sitting in the soil has developed rot, you can always take the pads attached to it and propagate those, but my sense is that as it gets warmer and you start giving it a little more water things should sort themselves out.
