Twilio charges less than a cent for each message. A hundred messages is 79c. I’d be surprised to find any other solution that is dramatically cheaper. On AWS it would be 58c.
Those prices are in US, but I would be surprised if those services weren’t competitive in other markets.
Any recent PC will do. Naturally, if you plan on playing games on it (moonlight and sunshine) you should size appropriately, and I’d recommend not to mix your NAS with a gaming PC since games and accessory can crash your server.
Without gaming, any 8th generation Intel or newer with iGPU should handle most transcoding needs. It’s more than capable of handling all the services you mentioned (again, not considering gaming)
I’d look into mobile class cpu so it’s lighter on energy consumption.