Well I recently just finished a two week suspension and when I returned I got no chat logs or emails telling me why I was. It's safe to assume that my ban was manually implemented by a Riot employee and that seems to be the case for you as well. However, it seems that they took the time to further review your account and upgrade the punishment you received; meaning that you have violated Summoners Code during ur chat restriction, or there was just a bunch of cases against you and the chat restriction only covered some of it.
You are lucky, as there have been cases where people received two week suspensions only to have them upgrade to perma bans given the amount of toxicity/violations towards riot's rules.
Had you said something like "during my chat restriction I never said anything" I would probably have a different stance on this, but being someone who has dealt with chat restrictions, I know you may have found a way to be toxic during that time.
Riot basically expects players to reform by having the players NOT EXPECT light punishments. What I mean is, any warning given by riot is a warning regardless. Whether its the automated email saying you are on borderline toxicity, or someone getting a two week suspension without having ever been given 1 day. 3 day or 1 week suspensions.
What you should do is wait off the two weeks.(Cause I doubt you will get bumped to a perma unless u have been reported for being toxic EVERYGAME since the chat restriction implemented) Make a new account if you want or just take a break. Clear your head, and when you return just mute the chat. Chatting in League of Legends is by far one of the easiest ways to receive punishments. And given that the things you type might not be toxic, others may not see it as such.
P.S. You can't say "I know I was toxic and deserved the chat restriction" then say "How do I get suspended for saying nothing?". It's clear you said something, the only room for error in this topic is When these things were said. If it's not an everygame thing, you can work past the two week suspension and reform easily.
P.S.S. Yes, it is highly possible your account was manually reviewed and had the punishment upgraded.