Perhaps consider that empirical evidence isn't the only form of evidence nor the only admissible form of evidence and that the way science interacts with other ways of knowing is open to criticism.
Sure. For example, there is also logical evidence (proof) and interview/eye-witness testimony but, of course, eye-witness testimony is the least reliable form of evidence by far.
There are examples that more severely show the limits of Popperian falsification. Such an example: Godel's incompleteness theorems are unfalsifiable. E.g. the second theorem can be proved in primitive recursive arithmetic, which means that its falsification would demonstrate the inconsistency of the theories that it applies to, but this is an even stronger result than it claimed.
So it's not even the case that empirical evidence is the ideal standard of evidence that we deviate from due to practical considerations. It is limited, period. Scientism is a philosophical sickness.
Godel's incompleteness theorem exists in a particular deductive system, it in no way holds weight outside of that system. His completeness theorem shows the mathematical logic is complete. Different deductive frameworks have different axioms.
All of which are essentially irrelevant to inductive systems like the natural sciences, for which Popper is writing.
I have never met nor even corresponded with a colleague who believes that empirical evidence has no limits (whatever that might mean). Again, the charge of scientism seems to be little more than a bogeyman to silence or shame rigorous thinkers.
When asked if science can, in principle, discover everything, I wouldn't even know how to respond. I'm not sure what such a question even means.
Scientists move forward in their research with the provisional assumption that progress can be made...what other option is there?
Perhaps consider that empirical evidence isn't the only form of evidence nor the only admissible form of evidence and that the way science interacts with other ways of knowing is open to criticism.