Ultimately, where your portfolio is hosted is less important than your portfolio itself. It should demonstrate your thinking, give a clear description of the brief, celebrate your ideas (and of course, have some beautiful visuals!)
This doesn’t need to be a website. Cloud based programmes are brilliant as you can use videos, there are no file size limits or heavy downloads in someone’s inbox. Just a handy link. Figma/Google slides are great free options. A click-through portfolio gives you control over how someone views your work, and allows you to tell a story. You lose that control on a website.
A really well curated deck will have the impact you want. I’d suggest building a new portfolio in one of those formats and heading to some reviews. There’s nothing more valuable than other creatives looking over your work. Practicing how to talk through it, making sure it’s easy to understand the brief and your solution. Creative Lives In Progress hosts portfolio reviews, and has a very handy guide on where to start creating your book.
If you’re looking for an alternative public portfolio, you could try creating a designated Instagram page for your work. That’s a free way of building your online presence — more often than not, if you Google your favourite creatives, their Instagram page is the top result. This allows you to send your page over to studios and they can get an instant idea of who you are as a designer. Then you can follow up with your full portfolio to blow them away.
I hope you find the right role for you.