There's nothing magic about a chinoise; at least when it comes to purees it might as well be an ordinary sieve. The finer the holes, the finer the puree. A chinoise is especially useful for pressing the "essence" out of cooked vegetable without forcing the too-cooked vegetables themselves into the stock, gravy, or sauce.
In the sieve class (which includes chinoise), the best tool for getting very fine purees is usually a tami because they can be bought with get such fine screens.
Food mills are in the same "not magic for purees" category. Mills are very good about separating skin and fiber, but in terms of really silky purees are unexceptional.
Stick blenders usually don't do ultra-smooth purees very well. They leave lumps except when used in tall, narrow containers with lots of liquid.
"Robot Coupe" is a professional-line food processor brand name. Robot Coupes don't do a better job than Cuisinart, Kitchen-Aid or whatever. From a results standpoint, all of the good food processors are pretty much the same.
If you want a really velvety puree, break up the cooked celeriac with a ricer, coarse sieve, chinoise, food mill or whatever, then pass it through a fine tami or fine sieve. Alternatively, do the whole thing in a food processor. It won't be the nth degree of smooth, but it will go a helluva lot faster. If you use a food processor, be careful not to overwork the celeriac or your puree will be gummy.
BDL