I've had dental work done and was only allowed to eat liquid and then soft food. I had to get creative with what I could eat - yes I did loose weight too.
It does depend on whether you are Type 1 or 2. If you are Type 1 then you have more flexibility.
The following is what I did as a Type 2: I grated cheese into my soup, it melts and doesn't affect it being liquid but adds calories. I ate sugar free jelly (although very little calories it does fill you up). I blitzed up tinned apples (10g carbs per 100g). Drink milk or make it into milky hot drinks. Ground rice pudding is good.
As the healing progressed, I went onto pate and cheese spread.
I wouldn't normally say this but sometimes you have to have less control over your blood sugars as you do not want to get an infection in the extraction site and need to eat the liquid and semi-solid food. Another thing you can do is to rinse with corsodyl after eating.
When I had my wisdom teeth out at the hospital years ago, the gums were stitched up, but other extractions I had at the dentist weren't and the reason they tell you about the liquid diet is to prevent a dry socket which is not very nice and needs antibiotics.