'Thus' is a useful linking word in formal writing, and you might hear it used when someone is reading a formal lecture or speech. It is never used in informal contexts, though. 'Thus' would sound very awkward and out of place in everyday conversation. In casual exchanges, we use 'so'.

I am an English learner too, so here I share the way I learnt to use the conjunction-like adverbs :) 1. …; thus, …. 2. …, and thus …. 3. …. Thus, … 4. …; S., thus, V. …. 5. …, and S., thus, V. …. 6. …. S., thus, V. …. e.g. He is not satisfied with our work; thus, we must prepare a new proposal. = He is not satisfied with our work, and thus we must prepare a new proposal. = He is not satisfied with our work. Thus, we must prepare a new proposal. = He is not satisfied with our work; we, thus, must prepare a new proposal. = He is not satisfied with our work, and we, thus, must prepare a new proposal. = He is not satisfied with our work. We, thus, must prepare a new proposal.

Hi Steve, I do thank you for your very detailed explanation. It is always a pleasure to read your answers ;-). Take care, Paul

Hi Henry, Many thanks for your help. Good luck with your own language studies! Regards, Paul

"Thus" sounds more formal than "for this reason" or "so" which is probably what you'd probably say in speech. Also, "thusly" isn't pejorative it's just the adverb form of "thus", meaning "doing something in such a manner".