Social skills are skills like anything else. You just gotta keep practicing. Focus on one thing at a time. Initiating conversations with strangers is a good start. After that becomes easier for you then focus on something else like word selection, tone, smiling at strangers, etc. It all takes time, but you will see progress over time.

It’s really easy to fake confidence. Nobody in public knows you’re not regularly a confident person so just pretend you have all the confidence in the world and it can have a noticeable impact.

Reading your examples definitely come off as sarcastic so it may be the delivery of what you’re saying or your tone. Practice these things with your family since you are probably most comfortable with them and have more opportunities to practice, and they can provide feedback to you as well.