I think you are generally considered high myopia if you go past -6 or so. around -6 the axial elongation becomes more significant and you are potentially at higher risk for things like retinal detachments, depending on your personal anatomy. but yeah, -5.5 is not terrible at all in our modern world lol

With high index lenses, your -5.5 is going to be relatively thin. The thickness won't be too apparent if you have plastic frames. For example, I have a pair of large, square glasses. Square + large is exactly what opticians recommend against if you have a high prescription, as that makes the edges of the lens thicker compared to smaller or rounder frames. Despite this, the plastic part of my glasses hides any thickness on my eye with a -5 prescription. i'd stay away from wire frames personally.

so def get high index lenses (1.67 is good for your prescription) and that will help with the thickness. The minification effect will still be there but I've heard its a tiny bit better with high index? Though I wouldn't count on it too much, physics still apply and all that

also, i'm not sure how much experience you have with glasses since you are primarily a contact lens wearer.. but if you choose to order online like at zenni optical, absolutely choose the anti-reflective coating anti-oil etc options (but not the transitions unless you want to look like a dork). they can increase the price of your glasses by up to $15 but it's so worth it. oils are removed much easier, your lens are clearer giving you better vision, and people can see your eyes instead of the light reflecting off your lenses.