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Sorry, it's not that kind of functions. I wrote a custom function in the function editor. I was learning how this feature works so I wrote this function that retrieves for each feature the number of filled fields (NULL values are set to be shown NULL). Here it is. This code adapted to the console returns right nb for each feature.

@qgsfunction(args=0, group='Custom')
def compta(value1, feature, parent):

    nb = 0
    for idx in range(len(feature.attributes())):
        attr = feature.attributes()[idx]
        if not attr == NULL : 
            nb = nb +1
    return nb

Seems like a caching issue. When classifying, the actual values of all attributes are fetched and the classification works correctly. However, the feature given to the user defined function compta() does not have the values filled in, so all features are counted as having no attributes set at all.

Probably an optimization to not fetch lots of stuff not needed for rendering anyway.

Thanks Sebastian for digging this.
Could this be related to #14273

Another interesting observation:

If you pass an attribute as a parameter, that attribute's value is available within feature.

@qgsfunction(args='auto', group='Custom')
def firstAttr(dummy, feature, parent):
    return feature.attributes()[0]

Make the expression firstAttr(123) and it always returns NULL when drawing a feature.
Make the expression firstAttr("NameOfFirstAttribute") and it returns the correct value when drawing a feature.

Sebastian - does it help if you alter
https://github.com/qgis/QGIS/blob/e9ef51341c2cef016648be6c619a4d43ffe362ca/python/core/__init__.py#L43

from
QgsExpression.Function.__init__(self, name, args, group, helptext, usesgeometry)

to
QgsExpression.Function.__init__(self, name, args, group, helptext, usesgeometry, [QgsFeatureRequest.AllAttributes])

?

does it help ...

Yes! The features are rendered correctly after that change.

I wonder if it could be an additional parameter to the @qgsfunction() what attributes the function expects to be filled. E.g.

@qgsfunction(args='auto', group='Custom', attrs=['attr1', 'attr2'])

@qgsfunction(args='auto', group='Custom', attrs=True)

Unconditionally loading all attribute values when a user defined function is used in an expression might be a regression for some people with large layers, many attributes and a function that does not use the attribute values at all.

Sounds reasonable. I'd open a PR and get Nathan to take a look, this is his baby ;)