here in gujarat it's just thick in consistency, dryness or wetness of the khichdi may vary across households so its ranged between slop to stew in thickness, usually it's thick enough that one has to jerk that big serving spoon hard to make it drop in thali,
then, it's served with a big spoon of oil / ghee, then it's mixed with fingers to get a preferred consistency and looseness,
things that can be served aside are, a piece or spoon of guud/jaggery, chopped onions, lehsun ki chutney, sometimes chopped mooli too,
then usually another sabzee or daal/kadhi is added to it to make that curry-rice like slop lol,
usually aalo-bengan ki sabzee goes bombastic with khichdi,
or kadhi as i mentioned before
well we also eat a lot of ghee with the khichuri, i think ghee+khichuri *IS* what makes me want khichuri and go through trouble of making it.
But its interesting how accompanyments vary significantly culturally.
In bengalis, its BIG NO NO to have torkari with khichuri - for one, we put fool-gobi, peas , beans, somtimes carrots in our khichuri so to have torkari with it is seen as a diss to the cook.
we usually have papad +beguni + a piece of fried rohu ( not eelish, that doesnt go together) or katla to go with it.
Some people will have achaar, indian style home-made potato-chips ( the crispy thin slivers we fry at home), pyaji - which is just fried onion fritter, some will add raw onions and mirchi as condiment on side but thats petty much all the variations of accompanyment of khichuri i have seen from us bongs.
personally, the crispy+buttery flavour of beguni goes so wonderfully well with the sloppy runny khichuri we like - if you havent tried that pairing, try it. Regular begun bhaaja is okay, but beguni...ufff.
Beguni isnt hard to make - you just cut baingan in thin long slices, dip it in besan and deep fry it.
PS: Also i think runny khichuri is slightly more nutritious than dry khichuri - because runny khichuri uses a LOT more dal in proportion to rice, so by proportion you are eating more dal than just blank carb white rice.