Now imagine that almost everyone communicates only via printed pamphlets, but pamphlet-printing business controlled by one censorious individual eager to push his agenda to the detriment of others. Could freedom of speech exists in such hypothetical society?
Your scenario isn't that hard to imagine. Back when most people did disseminate information using printed pamphlets, only a few people owned the printing presses that could manufacturing such pamphlets en masse. We survived as a species, even though those pamphlets were often inaccurate and inflammatory.
It isn't inconceivable to imagine dystopian future where everyone communicates using only 'social' media, and few corporations determine what is acceptable. In such future nobody has freedom of speech, and we get there with unwise individuals pushing for "Right to not get offended".
You are upset about a possible future regarding "communication", but communication requires two parties - one speaking, one listening - and optionally includes a third party - one to convey the information from the speaker to the listener. In all cases, speakers have the most limited rights, as it exists today and as it would be in your supposed society.
No speaker has the right to demand the service of any given conveyor or the ear of any given listener, except for limited common-carriers such as the postal service. (Even then, they must only carry your service if you pay for the transaction, similar to other common carriers such as the phone company that have to carry your speech if and only if you maintain an account with them.)
On the other hand, listeners very often have the right to decide who can speak with them. I can choose not to pick up my phone, add my phone to a Do Not Call list, and block your number, and even have you charged with harassment if you don't stop calling. I can't stop all junk mail, letters, and post cards, but I can throw them away without reading them. I can't stop you from holding up signs on a public street or shouting out to me as I walk past, but if you do these things at my house I have various resources (harassment laws, noise ordinances, zoning laws, soundproofing) that can block you from me.
In this society you describe, what you mean by "everyone communicates using only 'social' media" is that listeners confine themselves to their homes and only make themselves available via social media platforms, and those platforms choose to cater to listeners over speakers, and that you as a speaker won't be able to post signs or yell at listeners who don't want to hear you. Your freedom to speak does not and never has imposed an obligation to listen, and listeners can choose to (or empower others to) filter content they hear. The system works as intended.