Sorry to have discovered and answered this so late, but the answer is yes. They are nearly identical. There is, however, a difference in the battery height dimensions, which you can see in the plastic shim between the two layers of the Steel, yielding its 250mAh capacity. Also, the Time Steel’s screen is bonded to the glass. rather than separate from the frame.
Part number for the battery is SP551923AE. Looks like there might be replacements available from AliExpress; maybe not…
Dimensions I measured for the battery were:
With that in mind, I bought the following Lithium batteries:
Sadly realized the T-shaped pressure pad was nonstandard. Tried soldering to it and messed up. Ended up just buying a PTS with a broken screen on ebay and using its battery. You could also swap in a regular Time’s battery, but just get reduced battery life. Somebody else suggested: there’s a lot of replacement battery on internet. Just search “150mAh P11G7T-01-S01”. Would work with reduced battery life.
Best of luck.