I've sent weird SMS messages through my (rooted) phone before. Silent SMS messages (useful for police trying to activate your phone for triangulation) still returned delivery reports a year or two ago, allowing someone to find out if someone else's phone is on without the target ever noticing.

I think Android removed the ability to send more annoying messages through its normal APIs (like flash SMS messages) but if you have access to any modem (either a smartphone or a full ESP32 dev board costing <50 bucks on AliExpress for 4G LTE), you can bypass any such restriction.

Carrier firewalls will probably filter these messages out but I wouldn't rely on it.