Grammar check: further or farther – do you get it right?

I recently hesitated when I wrote the phrase “look no further,” referring to a search for Thanksgiving recipes. Was that correct? I thought back to the old rule reminding me that farther meant physical distance and further, well it’s different, but I couldn’t remember exactly why.

Jump to Grammarly, which explains it in detail, yet I’m still a little confused. Here is what seems clear to me about further and farther:

Farther connotes distance, but it can also refer to a more advanced point.

Both further and farther are adverbs, but further can also be a verb, as in, “She furthered her career” as well as an adjective, such as, “pursuing further information.” Still okay, but now things get murky:

Grammarly poses the question, “How do the definitions of farther and further overlap? Can you use further or farther away in the same way?” The answer:

“Some…