Ancestors may be Jewish along maternal line, but how far back is too far?

I have a great-great-great grandmother (1836-1920) with the last name Mechler which I read is a North German and Jewish surname. She lived in Germany, emigrated to the USA, and was married to and buried as a Catholic, and I don’t have information about her early life or parents yet, as our tree doesn’t yet go back that far.

I know it’s stereotypically silly for Americans to get excited about certain ancestral heritage. But to be honest I can’t hide the fact that I’m excited to find a Jewish name in my maternal tree. Is there any way to confirm that she or her family may have been Jewish? And secondly, if we can confirm it, what are the next steps? Is it too far back to celebrate and identify with Jewish heritage?