Can residents whose names are not on the lease agreement be considered original tenants?

I moved in to an apartment one year ago with 3 roommates. One of the roommates was the sole signer of a year lease. The year has passed and we are now month to month, but the roommate who signed the lease is moving out.

We emailed our landlord and told her we would like to sign a new lease, hoping that we could keep the rent price the same since we all moved in together at the start of the year lease. She responded by immediately listing the apartment on Craigslist for a 20% rent increase and said there will be showings starting on Sunday.

So she wants us to sign a new lease for a higher rent price. Is it lawful for our landlord to list the apartment for a higher price, effectively telling us that we can either sign for the new price or be kicked out in 30 days?

We believe that we may be “original tenants” which would qualify us for protection from rent increases. We’re reaching out to a tenant rights group but I’m wondering if anyone here can shed light on this.

I live in San Francisco.