Based on the description on their site, the controller includes a built-in battery: "8.39 Wh Li-ion battery, 35+ hours of gameplay… "
That was disappointing for me. Specially condidering the Steam Frame’s controllers make use of AA batteries: “One replaceable AA battery per controller, 40hr battery life”
AA Batteries might not be as convenient to use, but being able to replace them is a great advantage. All my Xbox360 controllers still work fine, but none of my PS3’ Dualshock 3s.
The official docking station could be used to recharge (rechargables) AA batteries so the functionality could remain the same.
If there’s a market for it, replacements will be made. You can buy a replacement PS5 battery for $5. You can also buy a iPhone 4 battery (still). LiPos are quite easy to make (geopolitics aside) so making one that fits is not hard at all.
The PS5 battery has a plug, if the Steam Controller is like that (probably is), the only tool required is a screwdriver, which seems like a great tradeoff to replace the battery every 5+ years instead of every week or two, and being able to recharge it easily and quickly.
Worst case scenario you have to use a generic battery that is about the right size instead of a perfect fit. Maybe a little less battery life but it’s still more than enough anyway.