The key to fish sauce is that it was used very, very widely. SE Asian fish sauce is the best-known survivor of this tradition. Fish sauce has also survived in the Mediterranean, with colatura di alici still being made in Italy. In East Asia (China, Korea, and Japan), soy sauce and bean pastes largely replaced fish sauce (and fermented meat and snail sauces), but fish sauces similar to SE Asian fish sauces continue to be made and used in Korea and Japan (usually made from sand lance or mackerel), and fermented seafood is used in some Chinese sauces, such as oyster sauce and others. There are also English sauces with fermented fish, notably Worcestershire sauce.

Less well-known are Indian, Iranian, Persian Gulf, Egyptian/Sudanese, and West African, and other fermented sauces and pastes made from fish and/or other seafood. In addition to sauces and pastes, there are also other fermented fish products such as fermented whole fish (which can be salted, dried, or frozen (frozen is traditional in Alaska for Yupik qassayaaq, "raw baby fish"), fermented fish heads (e.g., in Alaska), etc. Fermented fish products were common enough so that no connection was needed between the Mediterranean and SE Asia to explain both having such sauces. Whether or not fish sauces were independently discovered in different regions, or started in one place and spread is unknown, but because fish will ferment quite readily, independent discovery is likely.

For more on fish sauce, see:

• https://www.reddit.com/r/AskHistorians/comments/cv8ij1/is_there_a_historical_connection_between_roman/

As for Western pasta and East Asian noodles, the early history of both is opaque. We have much earlier evidence of noodles from East Asia but there are major differences between the earliest noodles (made from millet) and later East Asian noodles (made from elastic soft wheat dough) and Mediterranean pasta (made from non-elastic semolina dough when available). More generally, human have been making dough for at least 30,000 years (and possibly for much longer), and have been cooking by boiling for a very long time too, so boiled dough products such as pasta, noodles, and dumplings could easily have developed in many places around the world.

We know of no connection between Eastern and Western noodles/pastas. Perhaps there is one, but we have no evidence of any connection. IMO, there is no need to seek one - independent invention is very likely.

For more on pasta and noodles:

• https://www.reddit.com/r/AskHistorians/comments/ee0vrm/what_is_the_origin_of_pasta/

• https://www.reddit.com/r/AskHistorians/comments/alhtmy/which_came_first_asian_noodles_or_pastas/

Dumplings like manti/mantu/mandu have an unknown origin. What we know is that there is a dumpling tradition running from Eastern Europe and Turkey through to western China and Mongolia with a shared origin (and probably this continues to eastern China, Korea, and Japan). Where this comes from we know not. It might have come from western Asia or the Mediterranean, but probably didn't. As for the relationships between Persian dumplings, Turkic dumplings, and Chinese dumplings, all we can do is guess. It's possible that Persian and Chinese dumplings developed independently, and Turkic peoples copied one or the other, but they might all have a shared origin, and it's possibly originally Turkic. Mediterranean filled pasta appears to be independent - Turkic dumplings appear to have reached Anatolia after stuffed raviola was already around. (But it's hard to be sure, because a food might exist for a long time before we find it mentioned in cookbooks or recognisably described in writing.