from the bits and pieces I've read
Missed opportunity to write
qubits and pieces.

Moreover, in the future, bitcoin mining will not produce many bitcoins or bitcoin reserves will be completely mined, will "treasure hunters" become a new trend?
If my understanding of bitcoin history is correct, I don't think the rise of an emerging technology, like quantum computing in this case, is the first time it has created a little anxiety for bitcoin holders. The whole "treasure hunters" era you are describing is happening not only in the very present day, but in the past as well.
For example, in the early years I'm pretty sure people were concerned about bitcoin's fundamental cryptography, specifically the Elliptic Curve Digital Signature Algorithm, and how it might not be secure long-term. These concerns were kinda more philosophical in nature, whereas the quantum threat is more theoretical. I only say theoretical, not to mean impossible, but more so to mean not really feasible/practical in the world we currently live in. Math and current number of qubits (which are error prone, loud, and don't last a long time) tell a story that it could be a reality one day. Then you get into the conversation of "logical qubits", which are the ones that are relevant in terms of breaking cryptography/encryption, don't exist yet. If they do exist today, there would probably be only a couple of them in a highly experimental state.
Android RNG vulnerabilites scared a lot of people too, but that made sense since actual bitcoin was stolen for some. The ASIC miners also created a scare for bitcoin because people thought they could potentially cause a centralization of hashing power and possible 51% attacks. The whole thing about public key exposure and reusing an address also created fear for bitcoin, but solutions like good practices in not reusing the same address twice and utilizing hierarchical deterministic wallets put most folks at ease. When SHA-1 was demonstrated to be insufficient and weak, people started to immediately question SHA-256.
Honestly, someone should make a fear and greed index-type of display that estimates the current public's view of bitcoin's security and hardness. This shit just goes up and down and up and down for one reason or another. It never seems to end, lol. What will be the new scare after quantum computing threats are pacified? My guess will probably be government overreach and corruption. World leaders and powerful people who run private companies seem to have no issue with partaking in the human trafficking of minors. You think they are above forcing known individuals who possess lots of bitcoin to hand over their private keys?
Edit - Forgot to mention satoshi implementing mining difficulty into bitcoin in terms of answering your statement's regarding bitcoin being "completely mined". It's one of his most genius aspects of bitcoin, because it shows his awareness of exponential technological development/progression.