The diaspora and isolation has resulted in the evolution of countless new languages, English alone has spawned hundreds. Fortunately translation software is quite freely available and most Federation citizens have at the very least Augmented Reality glasses, if not cranial implants. Ships on which every crewman speaks a different language and does not know any of their shipmates’ tongues are not unknown, but very uncommon. The Federation has made numerous attempts to encourage solidarity and interplanetary cooperation by formulating a single “common tongue”, three of which are in common use.
Lojban is the official language of business and politics, however its incredible preciseness and linguistic isolation has prevented it from becoming an “everyday” language and its mostly used for contracts and laws.
Basic Anglic is a simplified version of English with all regional jargon stripped out and grammar greatly simplified. Anglic spelling is completely phonetic (funetik) with no silent letters or compound sounds. It is fairly commonly used for communication between individuals from different worlds and is probably the most prevalent “second language” and even a first language in some places, as a result it has mutated considerably.
Landlish is the naturally evolved language of SecLand, developed from a mix of English, Latin, Mandarin, and Lojban. It’s fiendishly complicated to learn as an adult but most inhabitants of the capital only know Landlish and maybe a smattering of Lojban and Anglic, and they’ve spread it to most planets linked by stargates.