I wouldn't count on a procedure being covered by a specialist copay, only office visits (like whatever consultation they do before they schedule the procedure).
This. You'll be billed for a "visit" when you go and talk to them and they maybe take a look at your body. If they actually
do anything, that will almost certainly be billed separately as a procedure. The procedure will likely be one of the things that brings the deductible/coinsurance formulas into play, rather than having a fixed copay, but that will be something you'd need to read the fine print on your plan documentation to get a better idea about.
The HSA plans on the other hand tend to be more standardized so we can pretty confidently say that you'll pay the full cost of this whole thing out of pocket until you hit your deductible, and then 20% afterward.
How to think about the choice here:
First off, it's important to recognize the difference between pre-tax dollars and post-tax dollars. Your premiums will generally be pre-tax dollars, and so will any money you have withheld for HSA or FSA. HSAs are great compared to FSAs because you lose FSA money you don't use by the end of the year, giving you an incentive to err on the side of under-contributing, whereas you can just blindly max out the HSA knowing you can use the money later if it's not needed this year. Do you even have access to an FSA?
All other out-of-pocket costs will generally be post-tax dollars. You'll need to scale these post-tax expenditures up by your marginal tax rate (including 7.65% payroll tax at most income levels) to get an apples-to-apples comparison.
Your HSA plan costs $39 * 26 paychecks (assuming biweekly pay schedule) = $1,014 before you have any actual medical bills. These are pre-tax dollars. Then you pay 100% of the first $4,000, and 20% of the next expenses until you hit your $6,350 max. If you're a single person maxing out your HSA the first $4,150 of these expenses can be pre-tax. Total medical bills of $15,750 or higher will cause you to pay the out-of-pocket max.
Premium for the medium plan is $94 * 26 = $2,444 pre-tax, and premium for the top plan is $123 * 26 = $3,198 pre-tax.
Seems like the medium plan should be a non-starter. If you have no medical expenses the medium plan costs $1,430 more in premiums. If you have $1 million in medical expenses the medium plan costs $1,430 more in premiums and $150 more in out-of-pocket costs. There isn't a place in between where the lines cross either. Same with the highest-priced plan. There are some amounts of medical bills where it would cost less than the medium plan, but it's not straightforward to think of a scenario where it would cost less than the HSA plan after you factor in the difference in premiums, and especially not after you factor in the tax savings from HSA contributions.
Now, this all assumes the network of physicians is the same between all of these plans. If the doctor you need is in-network for one of the plans but not the others, that can easily override all of the above considerations.