Looks like relay has burned out and now is permanently switched on. Should be repairable by replacing that white rectangle to a new one. Or better yet to replace them all, not to have more problems soon again.
My oven had similar problem. One relay was was leaking current when switched on and caused circuit breakers to go off. Exactly matching parts were only on AliExpress which is doubtful source. Found suitable replacement relay on Mouser from Omron. Just have to match coil voltage, switching current rate and body/pins sizes. Here is for example a datasheet for the one that I can see on the picture:
HF152FD/012-1H HONGFA RELAY
I would also replace all electrolitic capacitors on that board, also just in case. As these don't live long and the first candidates to be replaced on decades old devices.
And clean the board with something like IPA (isopropylalkohol).
Don't forget to turn off circuit breaker before disconnecting the oven from the mains. Make pictures before disconnecting everything. Or better yet a video that shows things under different angles. You need some dissoldering pump or hot air to remove those relay. Probably better to find someone who is more confident in this type of job if you have second thoughts.
As to your question, yes, you can probably use it as is if you disconnect one wire that goes from this board to heating element that is always on. Heating elements usually have some detachable connectors on them. Make sure you isolate the connector with electric tape and fix it to something so that it doesn't touch metal on metal anything. The reason why it should be safe is relays on ovens usually wired independently and have one wire in, one wire out. This is how they manage to be some kWatts of power and yet not to use heavy gauge cables but a lot of relatively small ones (1.5 or 2.5 mm2).
I wire all my kitchen myself and also repair them myself if needed. Expensive appliances are usually also better repairable. My father is EE and electronics was always my hobby. Saved a lot of thousands of euro this year (an oven, a washing machine, a tumb drier, a dishwasher, a gas water heater, an ADSL modem and a PC mainboard). All became broken one way or another after 9 years since we moved to our current apartment and bought them all brand new... amazing year.