Found multiple other cases when custom emmet snippets are not shown when their names partially entered.

It looks like it has something to do with the amount of the suggestions for the currently entered text. If the amount of suggestions is not big, then the custom snippet is shown among the suggestions. If the amount is big, the custom snippet is not shown until more text is entered and the amount of suggestions is reduced.

That way, entering ps won't show pstart, too many suggestions. But entering px will show pxtart, since there are not many suggestions.

My expectation is that my custom Emmet snippets should always be in the suggestion list, esp. when I entered a proper prefix of the entire snippet name.

It looks like it has something to do with the amount of the suggestions for the currently entered text

No. We show only the best match for the abbreviation/snippet that has been typed for Emmet

So in your case mrg fuzzy matches best with mr (See https://github.com/emmetio/snippets/blob/master/css.json#L137) than with mrgstart, and so you get margin-right which is the value for the snippet mr. This fuzzy matching occurs inside the emmet module called css-snippets-resolver

Similarly ps matches best with pos than pstart.

To learn more about fuzzy matching in Emmet for css, see https://github.com/emmetio/css-snippets-resolver/blob/master/index.js#L154

custom Emmet snippets should always be in the suggestion list, esp. when I entered a proper prefix of the entire snippet name.

That sounds reasonable. I can look into it

this will be fixed in tonight's Insiders (Sept 1)

Custom Emmet snippets(css) will always show up as long as what was typed is the prefix of the snippet name