I also noticed the difference the first time I put an EF lens with IS onto my R5 with IBIS. Together, they seem to stay on until the camera body goes into standby, which it does quickly because I usually have ECO mode active.
I still have an EF 100mm f/2.8L IS, and it behaves as you are describing.
There is an IS option which allows you to set the IS to be on only when taking "only at the moment of shooting," but I keep mine on so that it's active when I'm framing the shot. I like the EVF to be as steady as possible when I'm looking through it.
You will probably learn many tricks, over time, to save battery on your R5. For example, be careful about having the EVF and back screen switch automatically while you have the R5 slung over a shoulder. Every time your arm, strap, or a fold of your shirt get near the EVF proximity sensor, the EVF lights up, using mucho power. Plus, the activating I'm describing can prevent the camera from going into ECO mode, which, as you are finding out, keeps the IBIS/IS going and going.
Seems as if yours is normal, but it would be nice if others confirm.