All rights are only between an individual and their government

Different rights have different scopes. Some rights, like the right to live, are between everyone. Some others, like the right to receive a purchased product, are only between buyer and seller. Freedom of speech “just happens” to be between individual and government, in countries where it’s even a right.

The private property rights that give private companies the ability to censor your speech are created and inforced by the government in the first place, so functionally it’s not different. A handful of massive companies who functionally own the government getting to police what is acceptable speech is not functionally different from the government doing it directly.