Which could be considered an appropriate number of self-citations?

If the self-citations are pertinent and useful to the reader, no amount is excessive. If they are not pertinent or not useful, any amount is.

Use judgment when assessing whether your readers will find references to your own work more useful than possible alternatives, if there are any.

There is no problem with citing your own work, even in significant numbers, if the citations are relevant, and I wouldn't suggest removing any such references.

However, if a high percentage of the references are self-citations, that suggests that either you are not very familiar with other people's work in the area, or there are not many other people interested in what you are doing. Neither of these will give a favourable impression to reviewers, so it would be worth trying to find additional relevant references by other people.

Write the paper you think it should be written and cite what you use, whether from yourself or others. Let the reviewers and the editor complain if they think you are being excessive. But there is really no need to self censor, especially when you have done important work in the field.

And in any case, this might differ by field, etc.