I dont think the side effects are very common. The most common one is a sore at the injection site (a low grade fever is the other most common side effect, but since we rarely take our buns temp, this side effect probably largely goes unnoticed by the human).
My rabbits have been vaccinated with the myxo-rhd vaccin many times. I havent seen any side effects, but I know they sometimes occur. This year my bun got the new nobivac myxo rhd plus vaccine.
A long time ago my bun Bam got a reaction from either the old myxo vaccine, or the old rhd1, which were given on the same occasion. Those were the vaccines commonly used before the myxo-rhd came. My bun got two sores, 1 in each ear, and also a sore on one eyelid. This happened precisely 7 days after the vaccination. The sore on the eyelid healed quickly but if I recall correctly it took a month for the sores inside the ears to heal fully, which surprised me since they looked so superficial. My vet said the sores were probably a reaction to the vaccine.
I treated the sores twice daily by rinsing them with saline eye wash and applying fucidine ointment. My bun’s reaction seems rather similar to the side effects you are seeing. My bun never seemed to feel unwell and he never had problem with a vaccine again.