As of 2/10/2022, Prime Video still costs $8.99/month as a standalone service. Amazon has not announced an increase in the price of its streaming service.
Amazon did, however, announce an increase in the price of Amazon Prime. This subscription service gives you access to several perks, including free, fast delivery, Amazon deals, entertainment (including Prime Video), and more.
Amazon Prime will cost $139/year from March 2022, increasing by $20/year (up from $119/year).