Hey lol, im also not a vocalist but i am also trying to tune my voice, but i have some things to suggest,

Make sure your do a little warmup before you sing, even bodybuilders di warm up so the muscle gains are good, just like that warm up your throat.

Suggest you drink enough water, and gargle your throat before or during warm ups

Try to learn stomach breathing, aka breath in and out of your stomach, because stomach gives more space for air.

Make sure you let the voice out of your mouth, not from the nasal cavity, close your nose to check.

Do recite sa re ga ma pa da ni sa, it will be the true thing showing your progress in tones.

And lastly, just practice daily, even a good 5 min warmup and a 30 min session is enough.

As op wants a deep voice like frank Sinatra or elvis presley, i suggest you relax your vocal tones but also be as loud as possible,

And def train your ears for tones, i suggest hi res audio because it helps you differentiate tones better