I’m a goyish Palliative Care Nurse. How can I provide better care for Jewish patients and families in the future?

As per the title, I am a non-Jewish Palliative Care Nurse and I’m looking for some recommendations on how to provide culturally informed care to the Jewish population in my community. Any advice or recommendations on educational resources would be greatly appreciated.

With some baseline level research, I’ve seen that there is a special prayer that is recited for a member of the Jewish community after they pass called the Mourner’s Kaddish. According to google, the Kaddish is said by the closest family members of the individual, specifically their parents, siblings, children, and spouse, however, I have cared for a number of patients who have no immediate family anymore and I’m unsure if it would be disrespectful for a goy to recite the Kaddish. In the event that a Jewish patient has passed away, would it be appropriate for me to recite the Mourner’s Kaddish for them, or should I just reach out to a local synagogue so they can provide post-mortem rites?

Thank you for reading through my post, and I sincerely hope that someone can help point me to some resources to further my knowledge on this matter.

(Note: I plan to call a local synagogue tomorrow morning, since I waited too long this afternoon and I believe their phone line is now closed)