Senior (one step below staff in my company's hierarchy) engineer who does interviewing here. I don't know you, as you say, but I can tell you what I understand to typically separate junior, mid-level, and senior engineers (without making you wade through charts), and what I look for:
Senior is the "career level" for a software engineer - that is, it's the level you would expect most basically competent people to be at after 5-7 years of experience. The key difference between senior engineers and the lower levels is that seniors guide the planning process and technical architecture of the software they work on. They don't just or mainly do individual ticket work. As a senior engineer, I have multiple projects within my team for which I am the lead engineer or "feature owner". That is, I conceive the technical approach, I work with product managers and stakeholders to gather requirements and create and estimate the work. I do investigative engineering work to demonstrate the value and feasibility of the work being requested. I understand our systems to the point where I am comfortable devising high-level, large-scale modifications to their inner workings. I am also a mentor and guide for the other engineers on my team and in my organization.
Essentially, I am a mini-manager (of technology and planning, not people). The difference between me and a staff engineer is that I do this at an intra-team level; I don't do it for a whole business line or working group of multiple teams. I also probably spend a lot more time working on implementation of individual tickets than a staff engineer typically would, and less time monitoring or planning. The skillset is broadly similar, though.
If I am evaluating someone for a senior role, therefore, I am asking:
* Do they have a depth of knowledge which would make them effective doing that kind of technical leadership work?
* Do they have experience leading projects and/or architecting software, not just implementing tickets?
* Could I trust this person - after they've ramped up into our company - to independently do the above?
* Will this person be an effective mentor for other developers who are more junior than them?
* Will this person be able to communicate effectively with management and other stakeholders?
And I want to see examples of all of these things. I think that it's likely that, if you are being turned away for being "not senior enough," it's because you don't have or aren't making visible your experience in these areas.
Also, for what it's worth, when you mention:
> As one example, walking through my take home project one engineer asked me about a kind of React gotcha. I said I wasn't quite sure, and then he admitted that he only just come across that in their own code recently. But I felt like it had already counted against me, even though he himself hadn't known about it. I guess it felt like I should have been the perfect version of who they aren't yet.
If it actually counted against you, it is a yellow to red flag - but I ask these kinds of questions to assess how a candidate thinks about issues. I love it when a candidate says "I haven't experienced that, but the way you describe it suggests X Y so I'd look up Z and do A B C", or otherwise has a conversation about it with me.
Hope this is helpful!