However, near as I can figure, it offers no way to provision a second device with the same seed (or store the seed).
It's one of two sites that I use TFA for that I don't have a backup for, which is mildly annoying. I do have recovery codes, and will all too happily fall back on SMS.
For me, when I download Steam Authenticator it's tied to my phone number so the first time I login it will send me a text message code, and then from there it generates the authenticator codes in app
Well in the scenario where you lose access to your email address you would theoretically still have access to your phone with the steam app already installed and authenticated