I don't know about job ads you've seen, but senior manager is often a dream/wish of companies who'll hire the first person that won't make them facepalm during the interviews after 6 months of not finding the right senior.

> Where do I find companies that value and seek glue/leads?

I think most companies value such work; it's just important to find the language they use. For example, in my BU, we have agile scrum masters. They are doing essentially the same work as technical project managers in my previous BU from the same company. I'd just advise reading the ad language and deciding whether that's "glue you like" or not...

Get in the door as IC and then gradually and informally be social, ask to be in meetings, and do "free" glue work. If you're good at it and it's valued, over a few months you'll naturally be spending more time on that and slowly be assigned fewer and fewer IC tasks, after which you'll have a conversation with your manager about which direction you'd like to take, and then you're defacto glue even if that's not your job title. (I'm sure you could get a job title change if you wanted, but SWE may be a slightly higher pay scale than TPM. ;)

N.B. this advice is really for "normal" times; if you're remote it may be harder or easier to do the social part necessary, I have no idea.