I'd not suggest a complete profile rewamp. This is something that the clients may not like and give a go to.
I have been into the same place before, being a graphic designer myself(from a logo design expert to brochures and web designing based jobs mostly) , and what I did was to slowly migrate from one prime skill to another. Therefore, I'd suggest you start by adding a sperate web design portfolio on your Upwork profile, change your overview a little and emphasise your expertise at the new skill, add it in your skill set. In this way, you will neither lose the clients you have presently(graphic designing based) nor will miss out on the ones you wish to work with(web design focused). As the time goes, your profile will have more testimonials for the latest skills and you can then switch and make it your prime expertise.
I have started on Upwork with Logo design as my expertise and I mostly take up Brochure/Web designing jobs these days, and it all started with a good review for the brochures. Right now, yoiu can't just bid on the web designing jobs provided you've got no job history and a total rewamp might just confuse the clients. Slowly begin by adding new keywords on your job search, bid on them and let them see your good work. Once you gather enough testimonials, switch expertise and there you go!
When I hire freelancers, I hire specialists.
One of the main things I look for is their skill lists.
If I want to hire a web developer, I won't hire one who is also a writer or baker or graphic designer.
If I want to hire a graphic designer, I won't hire one who is also a translator or photographer or accountant.
But that's just me. Other clients may be more forgiving.
Then it's completely clear, you are not gonna hire me, ever.
Bcoz I'm a Graphic Designer + Web Designer + Video Editor..
No man, forget other clients, it is you who need to be more forgiving.
Its okay, just kidding.