If someone pays you money for your singing, you are a professional singer. Because you have a product they value. It’s that simple.
Someone will hire you because they are the prospective audience and they like what you do. Or they are a company believing that they can make money off of you, when they hire you to sing.
So what is that product? That is what you need to decide, put together and present. It is not your singing talent that they are going to pay for, it is how you have packaged your singing talent and have it for sale that will determine if you will be a professional singer.
For instance - if someone has a party and needs entertainment, they will look for an agency who can supply that, or they will look directly for acts that do what they are looking for.
If you are a great singer and pianist or guitarist and you have your own gear, you are self-contained. With a repertoire of a few hundred songs, and a clear image of who you are as an artist, you are now a product.
If you are a singer and don’t play an instrument, you either need to have musicians to collaborate with, or you can turn directly to an agency, send them a sample of what you look and sound like, and they’ll send you a list of songs that you need to know. When you get hired, you and everyone else they hired (who you may never have met before,) will show up, know the same 1,000 songs or so, know keys and parts for each of your instruments and voices, and together you will play the gig. You are a product valuable to the agency because you show up on time, know the material, and you sound and look the part, which together with the others makes up the product they sell.
Auditioning is the way to be seen to be considered for a part in musical theater. As a product you need to show that you are right for the role you are auditioning for, and in general you need to be a great singer, actor as well as dancer for musical theater. With a great head shot and a great agent you are well on your way.
As a solo artist you need original music, you need to both record it and perform it, and to "make it" you need a hit song. There is much more to it of course - but that's a start.
Regardless of how you want to make a living as a singer you need to present a product.
Do you need to be a great singer? Not all great artists are great singers or have great vocal technique. But to have a hundred people relying on you for their livelihood on a concert tour and fans waiting for you with their tickets in hand, it's a guarantee you don't want to worry about your voice. So yes, you do want to be a great singer with great vocal technique, because then you will not have any limitations to how far you can go, both when it comes to how big, and for how long.