Stainless steel spokes are the preferred type of spoke, and work extremely well in wheels that withstand huge loads. I wouldn't claim that those wanting greater strength should use carbon steel. Maybe in bolts carbon steel could be stronger as long as it doesn't corrode (example: 12.9 bolts), but the high quality of stainless steel used in spokes and the work hardening when drawing and butting makes the situation in spokes maybe not comparable to bolts. The highest quality stainless steels used by name brand manufacturers have been work hardened by drawing them into a wire and then work hardened even more by butting the spokes with a hammer, so the ultimate tensile strength and yield strength of those high-quality spokes will be huge, and in typical builds, they should be able to resist fatigue failure as well (but they do that better if you stress relieve the wheel).
Besides, in typical wheels, the limit of the load the wheel can withstand is caused by nipples self-loosening due to momentarily slack spokes. If the spokes are breaking but not self-loosening, it is most likely a combination of two factors, (1) you used no-name spokes as opposed to name brand (DT Swiss) spokes, (2) the spokes have not been stress relieved, as described in "The Bicycle Wheel" by Jobst Brandt. By using the best spokes you can find (DT Swiss triple butted stainless), you may be able to omit stress relieving. Jobst Brandt has said that the importance of stress relieving for durable wheels was discovered by using low quality spokes, and as materials improved, it became possible to build adequately durable wheels without stress relieving (but you should still stress relieve since it provides a margin of safety). Note that Jobst Brandt used 1.6mm midsection butted spokes and when stress relieved they didn't break in his wheels. If you use thicker butted spokes, the likelihood of spokes breaking is even lower.
You didn't mention using butted spokes in your question. This may also add to the likelihood of breaking spokes in addition to (1) and (2).
I would throw all your spokes away, replace them with DT Swiss Alpine III triple butted stainless steel 2.34mm/1.8mm/2.0mm spokes or maybe double butted 2.0mm/1.8mm/2.0mm spokes and build the wheel to a high and even spoke tension and then stress relieve.
My gravel bike is less than 2 years old and somehow I've broken all 7 of the rear-wheel, right-side, even-numbered spokes (the ones that see high tension on braking)
7*4 = 28. That is not an adequate number of spokes. The wheel may be able to be salvaged if you only use it for low loads. If you are overweight or carry lots of cargo on your bike, then I recommend replacing it with a 36-spoke wheel.
It appears that I may have fixed the wheel accidentally by using normal steel replacement spokes but I'm wondering if this indicates a problem with the design of the wheel.
Could have been a bad batch of spokes, or spokes from a no-name manufacturer, or lack of stress relieving or most likely a combination of all of these factors. 28 spokes is a problem in the design of the wheel, but still, a wheel that has so many spoke failures should be rebuilt entirely, with all spokes being replaced. Nipples can be reused if their threads are not damaged, rim can be reused, hub maybe can be reused but please make sure to lace it the same way if the hub flanges have been indented by high spoke tension. Actually, it might make sense to replace all spokes one by one, not all at once, to ensure it's laced the same way so the hub flange indentations will match the new spoking.
Since 28 spokes is marginal, triple butted stainless steel spokes from a name brand manufacturer are recommended, although your hub flanges may have been indented by non triple butted spokes so using normal butted spokes (example: by replacing 2.0mm/2.0mm/2.0mm spokes with 2.0mm/1.8mm/2.0mm spokes) might have benefits in this very special case of respoking an old hub. For new builds, always prefer triple butted.
Then, when all spokes have been replaced, remember to true and tension the wheel to a high and even spoke tension and then stress relieve the wheel.
Does mixing spoke types have any negative consequenses?
Not any major issues, but by mixing poor and good spokes the weakest spoke is the weakest link of the chain. Besides, if the old spokes have failed so much, all of them should ideally be replaced.