is deliverability purely based on the email server, or is it a combination between your domain/etc? I always wondered if it was YMMV for everyone saying different things about the different EMS out there (SendGrid, Mailgun, etc)

deliverability is actually incredibly complicated. Every mailbox provider (gmail, yahoo, hotmail/office365, comcast, etc... being the main ones) has their own algorithm for determining what is or isn't spam and includes things from user interaction to IP sending reputation to domain reputation to various types of authentication techniques (dmarc, dkim, spf, etc...)