WA landlord here. A coupe separate topics possibly happening at once:

It is legal and common for fixed time leases to automatically convert to month to month agreements at the end of the fixed lease if neither party ends the agreement. This is actually in a way to protect tenants from finding themselves out of a lease at the end. You don’t have to sign a new month to month lease agreement for it to be valid since you signed the fixed term agreement which contains the clause. And often the month to month is more expensive then the fixed lease, this is also normal and legal since it’s spelled out in your fixed lease agreement.

Raising the base rent. Since you automatically convert to the month to month at the end of your lease, the landlord can raise your month to month rent at the start of any month as long as they give 60 days notice if it’s in the city of Tacoma boundary. If it’s not in city of Tacoma proper it’s 30 days. If they gave you notice 60 days before the rent went up and it’s after the fixed term lease ended, that’s all that’s required to make it legal.

You don’t have to agree with the rent change for it to be legal - but your only two options in a month to month where proper notice has been given is: accept it by not canceling the month to month in writing. Or reject it by canceling the month to month in writing and move out before the end of the next month basically. Up to you!

The notice you received said that it was the new base rent for any lease renewals. The month to month clause is considered an automatic renewal. Therefore, the rent increase does apply. And they gave you 60 days notice. It is valid.