Exhaustion, frustration, and the breaking point — in everyday English
All of these expressions describe a person who has been pushed to their limit — a state mixing exhaustion, frustration, and the feeling that things simply cannot continue as they are. But they differ in important ways: some describe emotional collapse, others signal angry refusal, and others describe the exact moment the limit is crossed.
Burned out collocates naturally with completely, totally, utterly. The rope and tether idioms don't take degree adverbs as easily — you wouldn't normally say "I'm very at the end of my rope."
"I'm done" and "That's it" are very informal. "I've reached my limit" and "I've reached breaking point" are neutral enough for semi-formal writing or professional conversations.
Tether is strongly British; rope is strongly American. "I've reached breaking point" is more common in British English; "I'm at my breaking point" in American English. Both are understood globally.
Some expressions face inward — exhaustion, collapse (burned out, running on empty). Others face outward — anger, refusal (I've had enough, that's it). The same situation can produce either depending on personality.