I write my opinion as a Japanese native speaker. My major is not linguistics.
I think ”田舎育ちだからコンビニが珍しい” is also correct expression. but leaving “”珍しい” feels more literary style.
I think your sentence come from daily conversations (sentence-ending particle “さ” is mostly using in conversation ). So the sentence “田舎育ちだからコンビニが珍しくてさ” has a context. Japanese language is called high context language. In this case, I think there are other events or conversations that cause your sentence. for example,
In this example, what person A want to say is that 田舎育ちだからコンビニが珍しくて驚いた. So the i-adjective is conjugated.