I think the only salient facts anyone could offer here,
"If they would't be willing to pay me that, they wouldn't have proceeded anyway. Right?"
That one is wrong - they have absolutely nothing to lose other than a little time on their part.
(Say you had absolutely stated - perhaps in writing "To avoid time wasting, I just wanted to be absolutely clear that I absolutely will not take a position for less than X dollar salary ,not including any benefits whatsoever" - that would be different. But all you have at the moment is "some talk" on both side. Talk means almost nothing.)
So, your idea that they "wouldn't have proceeded", is, wrong.
Here are four general points that may be relevant:
1 - For better or worse, almost everyone "buckles" in salary negotiation (or any price negotiation). To take a "bitter" view of the situation, they're just "laughing at" the fact that you asked so much, and, they know very well you'll "take what you're offered" when it comes down to it.
2 - There is an insane demand for software engineers in most fields at the moment, at the time of writing. As a general principal, whatever you asked is almost certainly way, way too low.
(More on that. FWIW it seems to me there is a glut of low-level software engineers, but higher-level software engineers are non-existent, they can just write their own ticket. Just my experience in the particular areas I deal in, may be different for others.)
3 - You know at the moment they said "That seems a bit high." ..... If you think about it: what did you expect them to say? Whenever anyone mentions any price to me, whatsoever, in any context - even if I literally did not hear the price - I just say the words "that seems pretty high". What else would you say? (Conversely on the other end, I just instantly state "that's way too low".) So really, you can pretty much dismiss that they said "That seems a bit high..." in that early conversation.
4 - The absolutely overwhelming issue you face. In any and all negotiations, there is one, and only one, factor that entirely covers the total situation. You can only negotiate if you can walk. If they offer you X, and you have no alternative, what can you do? See point 1. The one and only way you can say No to X, is, if you have another offer (or are confident that you can get other offers in a reasonable time). Indeed, you can "poker-face" them (ie, you can pretend that you're willing/able to say no thanks and walk away), which is gutsy. But simply - in any negotiation - you need alternatives or you literally have zero negotiating power. In short at this time you should be seeking other real offers, as aggressively as humanly possible. Or else "they've got you". You know?
So maybe those four points are worth something to your situation.
Again the answer to you literal question (where you say "Right?") is that you're wrong on that one.
A handy tip: have you considered building more and more freelance jobs/contacts in the meantime? A great way to "not care" about fulltime offers is if you are pretty confident you can whistle up a good amount of freelance anytime. If you're a bit of a "hot shot", make it happen, then you really have the, well, income behind you to have "negotiating power".
Another handy tip: when companies want to underpay, and think they are dealing with a "tough negotiator", the first the place they go is ... offering "benefits". When you're paying for something, "benefits" are an ingenious negotiating tactic. "Benefits" simply cost less than "money paid out", and on the other side (almost all) people think "benefits" are worth more than they are. So be careful not to fall for the line "well we'll give you 'benefits' XYZ instead".