aaravchen I did not! Goddammit, thanks! I don't recall seeing this part during setup or it didn't jump out as a required step, but maybe I missed it. Afterwards though, this suggestion wasn't on any of their connection tips pages and I only just saw it now after deliberately looking for the info. I am assuming your phone works with no problems now.
Link, for anybody else in this situation: https://support.cape.co/hc/en-gb/articles/31333215956500-APN-Configuration-Guide.
I did not mess with IMSI protection at all since I was just trying to establish a solid connection and couldn't get past that part, but thanks, also good to know. I would like to keep the physical SIM slot open for use overseas with a local SIM card - most countries still do this though eSIMS will likely take over soon. So long as the extra eSIM or physical SIM can stay in the phone while inactive, that's fine.
I have another idle number from T-mobile on a physical SIM that I could transfer to Cape and play around with, but it has me considering side effects. I want to give Cape another shot, but not with my primary number - was out of pocket for about six hours and yesterday and just can't risk that again. Give it a few months and most of this stuff should be sorted out.
FYI to others who may switch back and forth, it not be a Cape problem, but when I brought the exact same phone back to T-mobile their activation team said it showed up in their system as a carrier-locked phone (it wasn't). Eventually we sorted it out when they saw just six or seven hours prior, that same phone was registered on their network as an unlocked phone. Not sure what it was that Cape (or I) may have done to it but that took time to fix on their end.