With a heat pump in an old building, you actually do save money, but the whole story is a bit more complicated than "insulation first, then heat pump." Heating costs have gone up, yeah, but whether a heat pump pays for itself really depends on your specific situation - and to be honest: a lot of the optimistic claims ignore the fact that old houses actually work differently than new builds.
The problem is less about efficiency itself than about reality. A heat pump runs better with low flow temperatures (around 35-45 degrees), but with older houses you often need 55-60 degrees because the big old radiators just demand it. That does make the heat pump less efficient, true. But: even with this "penalty," you'll do better economically as energy prices keep climbing than if you just keep going like you are now. The investment is steep - I'd estimate 15,000 to 25,000 euros, depending on the work involved and whether you need boreholes for ground source probes or just use air heat. There's state funding available, but it's gotten tricky lately, so get some proper advice on that.
A real energy audit (independent, not from a contractor who's trying to sell you something) is absolutely worth it - that's money well spent. They can tell you whether your house should be insulated first or whether a heat pump actually makes sense despite the old building handicap. Sometimes a hybrid solution works better: heat pump plus your old oil heating as backup for extremely cold days. That's possible too, but it's a different calculation again.