While discrimination in the workplace can manifest in indirect ways and would still be a problem, nothing you've mentioned leads me to believe that the events stem from your friend being a woman.
That being said, of course understand that I can only read the information as you presented it. Overall, I'm not saying management isn't making mistakes here (they are, and I would avoid them if I knew this during the interview process), but this doesn't seem to inherently suggest sexism.
To summarize the below feedback to your points; I disagree that this proves sexism. However, I cannot conclusively disprove sexism here either. The company is clearly making management mistakes with your friend. However, I am not able to judge whether that is purely because of bad management, or some underlying discriminatory reason. All I can remark is that you failed to point out any concrete instance where your friend's gender was the driving factor (but as mentioned before, sexism isn't always overt).
Her time-estimates are second-guessed or told they're wrong (we work together on them and I think they're optimistic). Her estimates have always (rare, I know) been proven to be accurate
I could tell you the same thing about companies I've worked at and I am male. Different managers, especially those who do not have the skillset of their direct reports; tend to wrongly estimate effort and time to delivery.
In official staffing documents, part-time contractors are counted towards her team whereas they are not counted towards other teams
You didn't really mention how this is a negative effect to begin with. However, in my experience as a consultant, whether I am treated similar to an employee or not varies based on the client. Some teams barely register that I'm not an internal employee, whereas other companies made it very clear that I'm not part of their internal employees.
Given there's no clear indication of how this is negative, this just seems like an inconsistency in the administration of the company, rather than a slight targeted at your friend.
Despite having a cross-functional team that interacts with many other teams and (very large) customers her meeting-schedule is gainsaid frequently
Again, nothing I haven't dealt with in my own experiences. I'm not saying management isn't making mistakes here, but this doesn't inherently suggest sexism.
Her team receives very high ratings by the organization, yet how and where she spends her time are questioned constantly
Having things questioned is not solely a matter of not being valued, and not specifically because of a discriminatory reason.
That being said, we hit upon the same issue here that I cannot conclusively prove nor disprove sexism. Could this be an indirect part of a larger sexist culture at the workplace? Definitely possible. Does your example concretely highlight this? Not in my opinion.
Her team is staffed exclusively by other women and LGBTQ+ folks,
Is the staffing an undeniably intentional "sorting" of employees to avoid "women and LGBTQ+ folks" in other parts of the company? That may be a case of discriminatory behavior; but it would be so towards the "women and LGBTQ+ folks" themselves, not specifically your friend as their lead.
and she was told that it was not a "high business priority" despite being very explicitly treated as such in project and revenue planning
Bad management; but nothing particular to sexism.
The company hired a somewhat mediocre male contractor (as full-time) as a senior engineer and at approximately the same time promoted a high-functioning female engineer to the same position, yet they paid the (now full-time) male contractor substantially more than the existing female engineer despite my friend's best efforts to get them the same salaries or similar packages.
Putting gender aside; contractors always tend to make more than internal employees.
Contractors have different taxation rates in their income compared to employees (as most contractors count as their own company), and they also live in a work regiment where there is less financial security. A contractor can be booted out of a company with less effort and cost to the company. This is one of the reasons why companies hire contractors, especially when they do not intend to employ them long term.
While this may not matter in your culture specifically, contractors also tend to not get paid leave and paid sick leave even when employees do.
To offset all of these considerations, contractors charge more by the hour in order to recoup the financial "losses" that they incur by not being a full time internal employee.
It's impossible to compare salaries of contractors and internal employees, as the surplus a contractor charges can be highly contextual based on (a) how urgently they needed a contract (b) how long they expect to be employed (c) how likely it is for the contract to be stopped at any time and (d) the business value of the work they deliver.
Internal employees and contractors are apples and oranges here.
Her manager, the director of engineering, told her that she would need to "work 70 hours a week for 3 years" to expect a promotion
Telling your friend this is sign of a bad workplace culture but not inherently sexism. Telling only the women this, and not the men (or telling the men otherwise) would be sexism.
despite the explicit company guidance that people are not expected to perform or rewarded for constant heroics
This sounds more like a matter of the company trying to put up a facade of "we don't crunch you for hours" to improve their image; while in reality still doing precisely that.
Not a great workplace culture, but not inherently sexist.
She was informed that she should not comment on or be concerned with the (mis)-treatment of another female employee because the other employee was not in her organization
Unless male employees were allowed to comment or be concerned with it, this is not sexism (towards your friend, not the other female employee).
Given that the other female employee is working for a different organization; this seems more like a rule to not comment on other companies that this company works with, so as not to create a dent in the working relationship these companies have.
Again, not particularly a positive management style; but I fail to see the sexism towards your friend.
Her manager informed her that his style was that of a "benevolent dictator," which we, in this context, interpreted as her not having any leeway to question his style
Management style aside; is this somehow different for the male direct reports of this manager? Unless that is the case, I fail to see sexism here, just an unproductive manager attitude.
She's given ambitious goals and when she accomplishes them is frequently informed that they weren't the correct goals or that things that fell below the cut-line (by agreement of the organization at the time, including her management) that they were "critical" and that they "slipped"
Not uniquely the female experience. Maybe (quite likely) disproportionately so; but we hit the same point of this being bad management, but it being unclear whether the underlying root cause is discriminatory in nature, or just a matter of (gender-blind) bad management.
Despite having executive experience and better qualifications than her manager, she was hired in under him
There is not enough information here to make a judgment call. The way you present it is similar to established cases of workplace sexism, but there are potential caveats. I cannot judge conclusively either way.
For example, if she was hired for her practical experience. The hierarchy in a company is not indicative of practical expertise when the core business is not management in and of itself.
As a software developer, I have worked under several managers/leads who had been either a mediocre developer or had never even been a developer; but who steered their careers towards management instead.
Another example is that employees who excel at their field tend to struggle more with career advancements that change their day to day skills. Why would a company benefit from having their A-list engineer promoted to being a fledgling manager where their non-engineering skills are either unproven or not as excellent as their engineering skills?
You could call this the curse of excellence. When you are so good at your job that there is no second and you are irreplaceable; then you tend to not be allowed to move to another place specifically because you are irreplaceable.