Face ID issue means Iphone needs formatting?

Yesterday my Iphone XS suddenly shut off and the apple logo has been blinking since. Given my phone is still under warranty I visited an authorized service provider (we don't have apple stores where I live) and the guy didn't even inspect it, he sluggishly told me it'll either need formatting or replacing. I informed him that the data was extremely important to me and I'd rather the format be the last option available but he said it's impossible. just like that. But is it really?

I didn't check my Iphone in and took it to another store (unauthorized -just for problem detection) who after taking his time to try find the issue said it was an face ID issue, and if the front camera got fixed it will go back to working normal like a charm. I looked up numurous videos/forums that mentioned the same problem.. apple logo blinking, face ID camera fixed, iphone back to normal.

Can someone please advice me what to do? Is the apple service representer really not bothering enough and I should raise it to someone else in the store or something???? I really don't feel comfortable handing in my iphone to get formatted knowing that there was an alternative that might work.

Any help would be highly appreciated